Solve the System of Equations 6x=7-2y 4x+y=4

$6 x = 7 - 2 y$ $4 x + y = 4$

Divide each term in $6 x = 7 - 2 y$ by $6$ and simplify.

Divide each term in $6 x = 7 - 2 y$ by $6$ .

$\frac{6 x}{6} = \frac{7}{6} + \frac{- 2 y}{6}$

$4 x + y = 4$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{7}{6} + \frac{- 2 y}{6}$

$4 x + y = 4$

Divide $x$ by $1$ .

$x = \frac{7}{6} + \frac{- 2 y}{6}$

$4 x + y = 4$

$x = \frac{7}{6} + \frac{- 2 y}{6}$

$4 x + y = 4$

$x = \frac{7}{6} + \frac{- 2 y}{6}$

$4 x + y = 4$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 2$ and $6$ .

Factor $2$ out of $- 2 y$ .

$x = \frac{7}{6} + \frac{2 (- y)}{6}$

$4 x + y = 4$

Cancel the common factors.

Factor $2$ out of $6$ .

$x = \frac{7}{6} + \frac{2 (- y)}{2 (3)}$

$4 x + y = 4$

Cancel the common factor.

$x = \frac{7}{6} + \frac{2 (- y)}{2 \cdot 3}$

$4 x + y = 4$

Rewrite the expression.

$x = \frac{7}{6} + \frac{- y}{3}$

$4 x + y = 4$

$x = \frac{7}{6} + \frac{- y}{3}$

$4 x + y = 4$

$x = \frac{7}{6} + \frac{- y}{3}$

$4 x + y = 4$

Move the negative in front of the fraction.

$x = \frac{7}{6} - \frac{y}{3}$

$4 x + y = 4$

$x = \frac{7}{6} - \frac{y}{3}$

$4 x + y = 4$

$x = \frac{7}{6} - \frac{y}{3}$

$4 x + y = 4$

$x = \frac{7}{6} - \frac{y}{3}$

$4 x + y = 4$

Replace all occurrences of $x$ with $\frac{7}{6} - \frac{y}{3}$ in each equation.

Replace all occurrences of $x$ in $4 x + y = 4$ with $\frac{7}{6} - \frac{y}{3}$ .

$4 (\frac{7}{6} - \frac{y}{3}) + y = 4$

$x = \frac{7}{6} - \frac{y}{3}$

Simplify the left side.

Simplify $4 (\frac{7}{6} - \frac{y}{3}) + y$ .

Simplify each term.

Apply the distributive property.

$4 (\frac{7}{6}) + 4 (- \frac{y}{3}) + y = 4$

$x = \frac{7}{6} - \frac{y}{3}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$2 (2) (\frac{7}{6}) + 4 (- \frac{y}{3}) + y = 4$

$x = \frac{7}{6} - \frac{y}{3}$

Factor $2$ out of $6$ .

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

$x = \frac{7}{6} - \frac{y}{3}$

Cancel the common factor.

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

$x = \frac{7}{6} - \frac{y}{3}$

Rewrite the expression.

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

$x = \frac{7}{6} - \frac{y}{3}$

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

$x = \frac{7}{6} - \frac{y}{3}$

Combine $2$ and $\frac{7}{3}$ .

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

$x = \frac{7}{6} - \frac{y}{3}$

Multiply $2$ by $7$ .

$\frac{14}{3} + 4 (- \frac{y}{3}) + y = 4$

$x = \frac{7}{6} - \frac{y}{3}$

Multiply $4 (- \frac{y}{3})$ .

Multiply $- 1$ by $4$ .

$\frac{14}{3} - 4 \frac{y}{3} + y = 4$

$x = \frac{7}{6} - \frac{y}{3}$

Combine $- 4$ and $\frac{y}{3}$ .

$\frac{14}{3} + \frac{- 4 y}{3} + y = 4$

$x = \frac{7}{6} - \frac{y}{3}$

$\frac{14}{3} + \frac{- 4 y}{3} + y = 4$

$x = \frac{7}{6} - \frac{y}{3}$

Move the negative in front of the fraction.

$\frac{14}{3} - \frac{4 y}{3} + y = 4$

$x = \frac{7}{6} - \frac{y}{3}$

$\frac{14}{3} - \frac{4 y}{3} + y = 4$

$x = \frac{7}{6} - \frac{y}{3}$

To write $y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{14}{3} - \frac{4 y}{3} + y \cdot \frac{3}{3} = 4$

$x = \frac{7}{6} - \frac{y}{3}$

Simplify terms.

Combine $y$ and $\frac{3}{3}$ .

$\frac{14}{3} - \frac{4 y}{3} + \frac{y \cdot 3}{3} = 4$

$x = \frac{7}{6} - \frac{y}{3}$

Combine the numerators over the common denominator.

$\frac{14}{3} + \frac{- 4 y + y \cdot 3}{3} = 4$

$x = \frac{7}{6} - \frac{y}{3}$

Combine the numerators over the common denominator.

$\frac{14 - 4 y + y \cdot 3}{3} = 4$

$x = \frac{7}{6} - \frac{y}{3}$

$\frac{14 - 4 y + y \cdot 3}{3} = 4$

$x = \frac{7}{6} - \frac{y}{3}$

Move $3$ to the left of $y$ .

$\frac{14 - 4 y + 3 y}{3} = 4$

$x = \frac{7}{6} - \frac{y}{3}$

Add $- 4 y$ and $3 y$ .

$\frac{14 - y}{3} = 4$

$x = \frac{7}{6} - \frac{y}{3}$

$\frac{14 - y}{3} = 4$

$x = \frac{7}{6} - \frac{y}{3}$

$\frac{14 - y}{3} = 4$

$x = \frac{7}{6} - \frac{y}{3}$

$\frac{14 - y}{3} = 4$

$x = \frac{7}{6} - \frac{y}{3}$

Solve for $y$ in $\frac{14 - y}{3} = 4$ .

Multiply both sides by $3$ .

$\frac{14 - y}{3} \cdot 3 = 4 \cdot 3$

$x = \frac{7}{6} - \frac{y}{3}$

Simplify.

Simplify the left side.

Simplify $\frac{14 - y}{3} \cdot 3$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{14 - y}{3} \cdot 3 = 4 \cdot 3$

$x = \frac{7}{6} - \frac{y}{3}$

Rewrite the expression.

$14 - y = 4 \cdot 3$

$x = \frac{7}{6} - \frac{y}{3}$

$14 - y = 4 \cdot 3$

$x = \frac{7}{6} - \frac{y}{3}$

Reorder $14$ and $- y$ .

$- y + 14 = 4 \cdot 3$

$x = \frac{7}{6} - \frac{y}{3}$

$- y + 14 = 4 \cdot 3$

$x = \frac{7}{6} - \frac{y}{3}$

$- y + 14 = 4 \cdot 3$

$x = \frac{7}{6} - \frac{y}{3}$

Simplify the right side.

Multiply $4$ by $3$ .

$- y + 14 = 12$

$x = \frac{7}{6} - \frac{y}{3}$

$- y + 14 = 12$

$x = \frac{7}{6} - \frac{y}{3}$

$- y + 14 = 12$

$x = \frac{7}{6} - \frac{y}{3}$

Solve for $y$ .

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

Subtract $14$ from both sides of the equation.

$- y = 12 - 14$

$x = \frac{7}{6} - \frac{y}{3}$

Subtract $14$ from $12$ .

$- y = - 2$

$x = \frac{7}{6} - \frac{y}{3}$

$- y = - 2$

$x = \frac{7}{6} - \frac{y}{3}$

Divide each term in $- y = - 2$ by $- 1$ and simplify.

Divide each term in $- y = - 2$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 2}{- 1}$

$x = \frac{7}{6} - \frac{y}{3}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 2}{- 1}$

$x = \frac{7}{6} - \frac{y}{3}$

Divide $y$ by $1$ .

$y = \frac{- 2}{- 1}$

$x = \frac{7}{6} - \frac{y}{3}$

$y = \frac{- 2}{- 1}$

$x = \frac{7}{6} - \frac{y}{3}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$y = 2$

$x = \frac{7}{6} - \frac{y}{3}$

$y = 2$

$x = \frac{7}{6} - \frac{y}{3}$

$y = 2$

$x = \frac{7}{6} - \frac{y}{3}$

$y = 2$

$x = \frac{7}{6} - \frac{y}{3}$

$y = 2$

$x = \frac{7}{6} - \frac{y}{3}$

Replace all occurrences of $y$ with $2$ in each equation.

Replace all occurrences of $y$ in $x = \frac{7}{6} - \frac{y}{3}$ with $2$ .

$x = \frac{7}{6} - \frac{2}{3}$

$y = 2$

Simplify the right side.

Simplify $\frac{7}{6} - \frac{2}{3}$ .

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{7}{6} - \frac{2}{3} \cdot \frac{2}{2}$

$y = 2$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

$x = \frac{7}{6} - \frac{2 \cdot 2}{3 \cdot 2}$

$y = 2$

Multiply $3$ by $2$ .

$x = \frac{7}{6} - \frac{2 \cdot 2}{6}$

$y = 2$

$x = \frac{7}{6} - \frac{2 \cdot 2}{6}$

$y = 2$

Combine the numerators over the common denominator.

$x = \frac{7 - 2 \cdot 2}{6}$

$y = 2$

Simplify the numerator.

Multiply $- 2$ by $2$ .

$x = \frac{7 - 4}{6}$

$y = 2$

Subtract $4$ from $7$ .

$x = \frac{3}{6}$

$y = 2$

$x = \frac{3}{6}$

$y = 2$

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$x = \frac{3 (1)}{6}$

$y = 2$

Cancel the common factors.

Factor $3$ out of $6$ .

$x = \frac{3 \cdot 1}{3 \cdot 2}$

$y = 2$

Cancel the common factor.

$x = \frac{3 \cdot 1}{3 \cdot 2}$

$y = 2$

Rewrite the expression.

$x = \frac{1}{2}$

$y = 2$

$x = \frac{1}{2}$

$y = 2$

$x = \frac{1}{2}$

$y = 2$

$x = \frac{1}{2}$

$y = 2$

$x = \frac{1}{2}$

$y = 2$

$x = \frac{1}{2}$

$y = 2$

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

$(\frac{1}{2}, 2)$

The result can be shown in multiple forms.

Point Form:

$(\frac{1}{2}, 2)$

Equation Form:

$x = \frac{1}{2}, y = 2$

Solve the System of Equations 6x=7-2y 4x+y=4

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