Solve the System of Equations x-(3x+4)/7=(y+2)/3 2y-(5x+4)/11=(x+24)/2

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$ $2 y - \frac{5 x + 4}{11} = \frac{x + 24}{2}$

Step 1

Solve for $x$ in $2 y - \frac{5 x + 4}{11} = \frac{x + 24}{2}$ .

Multiply both sides by $2$ .

$(2 y - \frac{5 x + 4}{11}) \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Simplify.

Simplify the left side.

Simplify $(2 y - \frac{5 x + 4}{11}) \cdot 2$ .

To write $2 y$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$(2 y \cdot \frac{11}{11} - \frac{5 x + 4}{11}) \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Simplify terms.

Combine $2 y$ and $\frac{11}{11}$ .

$(\frac{2 y \cdot 11}{11} - \frac{5 x + 4}{11}) \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Combine the numerators over the common denominator.

$\frac{2 y \cdot 11 - (5 x + 4)}{11} \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{2 y \cdot 11 - (5 x + 4)}{11} \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Simplify the numerator.

Multiply $11$ by $2$ .

$\frac{22 y - (5 x + 4)}{11} \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Apply the distributive property.

$\frac{22 y - (5 x) - 1 \cdot 4}{11} \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Multiply $5$ by $- 1$ .

$\frac{22 y - 5 x - 1 \cdot 4}{11} \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Multiply $- 1$ by $4$ .

$\frac{22 y - 5 x - 4}{11} \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{22 y - 5 x - 4}{11} \cdot 2 = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Combine fractions.

Combine $\frac{22 y - 5 x - 4}{11}$ and $2$ .

$\frac{(22 y - 5 x - 4) \cdot 2}{11} = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Move $2$ to the left of $22 y - 5 x - 4$ .

$\frac{2 (22 y - 5 x - 4)}{11} = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{2 (22 y - 5 x - 4)}{11} = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{2 (22 y - 5 x - 4)}{11} = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{2 (22 y - 5 x - 4)}{11} = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (22 y - 5 x - 4)}{11} = \frac{x + 24}{2} \cdot 2$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Rewrite the expression.

$\frac{2 (22 y - 5 x - 4)}{11} = x + 24$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{2 (22 y - 5 x - 4)}{11} = x + 24$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{2 (22 y - 5 x - 4)}{11} = x + 24$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$\frac{2 (22 y - 5 x - 4)}{11} = x + 24$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Solve for $x$ .

Multiply both sides by $11$ .

$\frac{2 (22 y - 5 x - 4)}{11} \cdot 11 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Simplify.

Simplify the left side.

Simplify $\frac{2 (22 y - 5 x - 4)}{11} \cdot 11$ .

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{2 (22 y - 5 x - 4)}{11} \cdot 11 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Rewrite the expression.

$2 (22 y - 5 x - 4) = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$2 (22 y - 5 x - 4) = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Apply the distributive property.

$2 (22 y) + 2 (- 5 x) + 2 \cdot - 4 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Simplify.

Multiply $22$ by $2$ .

$44 y + 2 (- 5 x) + 2 \cdot - 4 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Multiply $- 5$ by $2$ .

$44 y - 10 x + 2 \cdot - 4 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Multiply $2$ by $- 4$ .

$44 y - 10 x - 8 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$44 y - 10 x - 8 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Reorder $44 y$ and $- 10 x$ .

$- 10 x + 44 y - 8 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 10 x + 44 y - 8 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 10 x + 44 y - 8 = (x + 24) \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Simplify the right side.

Simplify $(x + 24) \cdot 11$ .

Apply the distributive property.

$- 10 x + 44 y - 8 = x \cdot 11 + 24 \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Simplify the expression.

Move $11$ to the left of $x$ .

$- 10 x + 44 y - 8 = 11 \cdot x + 24 \cdot 11$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Multiply $24$ by $11$ .

$- 10 x + 44 y - 8 = 11 x + 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 10 x + 44 y - 8 = 11 x + 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 10 x + 44 y - 8 = 11 x + 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 10 x + 44 y - 8 = 11 x + 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 10 x + 44 y - 8 = 11 x + 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $11 x$ from both sides of the equation.

$- 10 x + 44 y - 8 - 11 x = 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Subtract $11 x$ from $- 10 x$ .

$- 21 x + 44 y - 8 = 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 21 x + 44 y - 8 = 264$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Move all terms not containing $x$ to the right side of the equation.

Subtract $44 y$ from both sides of the equation.

$- 21 x - 8 = 264 - 44 y$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Add $8$ to both sides of the equation.

$- 21 x = 264 - 44 y + 8$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Add $264$ and $8$ .

$- 21 x = - 44 y + 272$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$- 21 x = - 44 y + 272$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Divide each term in $- 21 x = - 44 y + 272$ by $- 21$ and simplify.

Divide each term in $- 21 x = - 44 y + 272$ by $- 21$ .

$\frac{- 21 x}{- 21} = \frac{- 44 y}{- 21} + \frac{272}{- 21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Simplify the left side.

Cancel the common factor of $- 21$ .

Cancel the common factor.

$\frac{- 21 x}{- 21} = \frac{- 44 y}{- 21} + \frac{272}{- 21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Divide $x$ by $1$ .

$x = \frac{- 44 y}{- 21} + \frac{272}{- 21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{- 44 y}{- 21} + \frac{272}{- 21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{- 44 y}{- 21} + \frac{272}{- 21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$x = \frac{(44) y}{21} + \frac{272}{- 21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Move the negative in front of the fraction.

$x = \frac{44 y}{21} - \frac{272}{21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$

Step 2

Replace all occurrences of $x$ with $\frac{44 y}{21} - \frac{272}{21}$ in each equation.

Replace all occurrences of $x$ in $x - \frac{3 x + 4}{7} = \frac{y + 2}{3}$ with $\frac{44 y}{21} - \frac{272}{21}$ .

$(\frac{44 y}{21} - \frac{272}{21}) - \frac{3 (\frac{44 y}{21} - \frac{272}{21}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Simplify the left side.

Simplify $(\frac{44 y}{21} - \frac{272}{21}) - \frac{3 (\frac{44 y}{21} - \frac{272}{21}) + 4}{7}$ .

Simplify each term.

Simplify the numerator.

Apply the distributive property.

$\frac{44 y}{21} - \frac{272}{21} - \frac{3 (\frac{44 y}{21}) + 3 (- \frac{272}{21}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Cancel the common factor of $3$ .

Factor $3$ out of $21$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{3 (\frac{44 y}{3 (7)}) + 3 (- \frac{272}{21}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Cancel the common factor.

$\frac{44 y}{21} - \frac{272}{21} - \frac{3 (\frac{44 y}{3 \cdot 7}) + 3 (- \frac{272}{21}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Rewrite the expression.

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + 3 (- \frac{272}{21}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + 3 (- \frac{272}{21}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{272}{21}$ into the numerator.

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + 3 (\frac{- 272}{21}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Factor $3$ out of $21$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + 3 (\frac{- 272}{3 (7)}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Cancel the common factor.

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + 3 (\frac{- 272}{3 \cdot 7}) + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Rewrite the expression.

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + \frac{- 272}{7} + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + \frac{- 272}{7} + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Move the negative in front of the fraction.

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} - \frac{272}{7} + 4}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

To write $4$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} - \frac{272}{7} + 4 \cdot \frac{7}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Combine $4$ and $\frac{7}{7}$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} - \frac{272}{7} + \frac{4 \cdot 7}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Combine the numerators over the common denominator.

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + \frac{- 272 + 4 \cdot 7}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Simplify the numerator.

Multiply $4$ by $7$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + \frac{- 272 + 28}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Add $- 272$ and $28$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + \frac{- 244}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y}{7} + \frac{- 244}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Combine the numerators over the common denominator.

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{44 y - 244}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Factor $4$ out of $44 y - 244$ .

Factor $4$ out of $44 y$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{4 (11 y) - 244}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Factor $4$ out of $- 244$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{4 (11 y) + 4 (- 61)}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Factor $4$ out of $4 (11 y) + 4 (- 61)$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{4 (11 y - 61)}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{4 (11 y - 61)}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y}{21} - \frac{272}{21} - \frac{\frac{4 (11 y - 61)}{7}}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{44 y}{21} - \frac{272}{21} - (\frac{4 (11 y - 61)}{7} \cdot \frac{1}{7}) = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply $\frac{4 (11 y - 61)}{7} \cdot \frac{1}{7}$ .

Multiply $\frac{4 (11 y - 61)}{7}$ by $\frac{1}{7}$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{4 (11 y - 61)}{7 \cdot 7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply $7$ by $7$ .

$\frac{44 y}{21} - \frac{272}{21} - \frac{4 (11 y - 61)}{49} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y}{21} - \frac{272}{21} - \frac{4 (11 y - 61)}{49} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y}{21} - \frac{272}{21} - \frac{4 (11 y - 61)}{49} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

To write $\frac{44 y}{21}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{44 y}{21} \cdot \frac{7}{7} - \frac{4 (11 y - 61)}{49} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

To write $- \frac{4 (11 y - 61)}{49}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{44 y}{21} \cdot \frac{7}{7} - \frac{4 (11 y - 61)}{49} \cdot \frac{3}{3} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Write each expression with a common denominator of $147$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{44 y}{21}$ by $\frac{7}{7}$ .

$\frac{44 y \cdot 7}{21 \cdot 7} - \frac{4 (11 y - 61)}{49} \cdot \frac{3}{3} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply $21$ by $7$ .

$\frac{44 y \cdot 7}{147} - \frac{4 (11 y - 61)}{49} \cdot \frac{3}{3} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply $\frac{4 (11 y - 61)}{49}$ by $\frac{3}{3}$ .

$\frac{44 y \cdot 7}{147} - \frac{4 (11 y - 61) \cdot 3}{49 \cdot 3} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply $49$ by $3$ .

$\frac{44 y \cdot 7}{147} - \frac{4 (11 y - 61) \cdot 3}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{44 y \cdot 7}{147} - \frac{4 (11 y - 61) \cdot 3}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Combine the numerators over the common denominator.

$\frac{44 y \cdot 7 - 4 (11 y - 61) \cdot 3}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Simplify the numerator.

Factor $4$ out of $44 y \cdot 7 - 4 (11 y - 61) \cdot 3$ .

Factor $4$ out of $44 y \cdot 7$ .

$\frac{4 (11 y \cdot 7) - 4 (11 y - 61) \cdot 3}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Factor $4$ out of $- 4 (11 y - 61) \cdot 3$ .

$\frac{4 (11 y \cdot 7) + 4 (- (11 y - 61) \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Factor $4$ out of $4 (11 y \cdot 7) + 4 (- (11 y - 61) \cdot 3)$ .

$\frac{4 (11 y \cdot 7 - (11 y - 61) \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (11 y \cdot 7 - (11 y - 61) \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply $7$ by $11$ .

$\frac{4 (77 y - (11 y - 61) \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Apply the distributive property.

$\frac{4 (77 y + (- (11 y) + 61) \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply $11$ by $- 1$ .

$\frac{4 (77 y + (- 11 y + 61) \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply $- 1$ by $- 61$ .

$\frac{4 (77 y + (- 11 y + 61) \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Apply the distributive property.

$\frac{4 (77 y - 11 y \cdot 3 + 61 \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply $3$ by $- 11$ .

$\frac{4 (77 y - 33 y + 61 \cdot 3)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply $61$ by $3$ .

$\frac{4 (77 y - 33 y + 183)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Subtract $33 y$ from $77 y$ .

$\frac{4 (44 y + 183)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (44 y + 183)}{147} - \frac{272}{21} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

To write $- \frac{272}{21}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{4 (44 y + 183)}{147} - \frac{272}{21} \cdot \frac{7}{7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Write each expression with a common denominator of $147$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{272}{21}$ by $\frac{7}{7}$ .

$\frac{4 (44 y + 183)}{147} - \frac{272 \cdot 7}{21 \cdot 7} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply $21$ by $7$ .

$\frac{4 (44 y + 183)}{147} - \frac{272 \cdot 7}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (44 y + 183)}{147} - \frac{272 \cdot 7}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Combine the numerators over the common denominator.

$\frac{4 (44 y + 183) - 272 \cdot 7}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Simplify the numerator.

Factor $4$ out of $4 (44 y + 183) - 272 \cdot 7$ .

Factor $4$ out of $- 272 \cdot 7$ .

$\frac{4 (44 y + 183) + 4 (- 68 \cdot 7)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Factor $4$ out of $4 (44 y + 183) + 4 (- 68 \cdot 7)$ .

$\frac{4 (44 y + 183 - 68 \cdot 7)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (44 y + 183 - 68 \cdot 7)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply $- 68$ by $7$ .

$\frac{4 (44 y + 183 - 476)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Subtract $476$ from $183$ .

$\frac{4 (44 y - 293)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (44 y - 293)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (44 y - 293)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (44 y - 293)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$\frac{4 (44 y - 293)}{147} = \frac{y + 2}{3}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 3

Solve for $y$ in $\frac{4 (44 y - 293)}{147} = \frac{y + 2}{3}$ .

Multiply both sides by $147$ .

$\frac{4 (44 y - 293)}{147} \cdot 147 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

Simplify.

Simplify the left side.

Simplify $\frac{4 (44 y - 293)}{147} \cdot 147$ .

Cancel the common factor of $147$ .

Cancel the common factor.

$\frac{4 (44 y - 293)}{147} \cdot 147 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

Rewrite the expression.

$4 (44 y - 293) = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

$4 (44 y - 293) = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

Apply the distributive property.

$4 (44 y) + 4 \cdot - 293 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply.

Multiply $44$ by $4$ .

$176 y + 4 \cdot - 293 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply $4$ by $- 293$ .

$176 y - 1172 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = \frac{y + 2}{3} \cdot 147$

$x = \frac{44 y}{21} - \frac{272}{21}$

Simplify the right side.

Simplify $\frac{y + 2}{3} \cdot 147$ .

Cancel the common factor of $3$ .

Factor $3$ out of $147$ .

$176 y - 1172 = \frac{y + 2}{3} \cdot (3 (49))$

$x = \frac{44 y}{21} - \frac{272}{21}$

Cancel the common factor.

$176 y - 1172 = \frac{y + 2}{3} \cdot (3 \cdot 49)$

$x = \frac{44 y}{21} - \frac{272}{21}$

Rewrite the expression.

$176 y - 1172 = (y + 2) \cdot 49$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = (y + 2) \cdot 49$

$x = \frac{44 y}{21} - \frac{272}{21}$

Apply the distributive property.

$176 y - 1172 = y \cdot 49 + 2 \cdot 49$

$x = \frac{44 y}{21} - \frac{272}{21}$

Simplify the expression.

Move $49$ to the left of $y$ .

$176 y - 1172 = 49 \cdot y + 2 \cdot 49$

$x = \frac{44 y}{21} - \frac{272}{21}$

Multiply $2$ by $49$ .

$176 y - 1172 = 49 y + 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = 49 y + 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = 49 y + 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = 49 y + 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

$176 y - 1172 = 49 y + 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

Solve for $y$ .

Move all terms containing $y$ to the left side of the equation.

Subtract $49 y$ from both sides of the equation.

$176 y - 1172 - 49 y = 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

Subtract $49 y$ from $176 y$ .

$127 y - 1172 = 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

$127 y - 1172 = 98$

$x = \frac{44 y}{21} - \frac{272}{21}$

Move all terms not containing $y$ to the right side of the equation.

Add $1172$ to both sides of the equation.

$127 y = 98 + 1172$

$x = \frac{44 y}{21} - \frac{272}{21}$

Add $98$ and $1172$ .

$127 y = 1270$

$x = \frac{44 y}{21} - \frac{272}{21}$

$127 y = 1270$

$x = \frac{44 y}{21} - \frac{272}{21}$

Divide each term in $127 y = 1270$ by $127$ and simplify.

Divide each term in $127 y = 1270$ by $127$ .

$\frac{127 y}{127} = \frac{1270}{127}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Simplify the left side.

Cancel the common factor of $127$ .

Cancel the common factor.

$\frac{127 y}{127} = \frac{1270}{127}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Divide $y$ by $1$ .

$y = \frac{1270}{127}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$y = \frac{1270}{127}$

$x = \frac{44 y}{21} - \frac{272}{21}$

$y = \frac{1270}{127}$

$x = \frac{44 y}{21} - \frac{272}{21}$

Simplify the right side.

Divide $1270$ by $127$ .

$y = 10$

$x = \frac{44 y}{21} - \frac{272}{21}$

$y = 10$

$x = \frac{44 y}{21} - \frac{272}{21}$

$y = 10$

$x = \frac{44 y}{21} - \frac{272}{21}$

$y = 10$

$x = \frac{44 y}{21} - \frac{272}{21}$

$y = 10$

$x = \frac{44 y}{21} - \frac{272}{21}$

Step 4

Replace all occurrences of $y$ with $10$ in each equation.

Replace all occurrences of $y$ in $x = \frac{44 y}{21} - \frac{272}{21}$ with $10$ .

$x = \frac{44 (10)}{21} - \frac{272}{21}$

$y = 10$

Simplify the right side.

Simplify $\frac{44 (10)}{21} - \frac{272}{21}$ .

Combine the numerators over the common denominator.

$x = \frac{44 (10) - 272}{21}$

$y = 10$

Simplify the expression.

Multiply $44$ by $10$ .

$x = \frac{440 - 272}{21}$

$y = 10$

Subtract $272$ from $440$ .

$x = \frac{168}{21}$

$y = 10$

Divide $168$ by $21$ .

$x = 8$

$y = 10$

$x = 8$

$y = 10$

$x = 8$

$y = 10$

$x = 8$

$y = 10$

$x = 8$

$y = 10$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(8, 10)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(8, 10)$

Equation Form:

$x = 8, y = 10$

Step 7

Solve the System of Equations x-(3x+4)/7=(y+2)/3 2y-(5x+4)/11=(x+24)/2

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