Solve by Substitution 7x+2y=24 , 8x+2y=30

$7 x + 2 y = 24$ , $8 x + 2 y = 30$

Step 1

Solve for $x$ in $7 x + 2 y = 24$ .

Subtract $2 y$ from both sides of the equation.

$7 x = 24 - 2 y$

$8 x + 2 y = 30$

Divide each term in $7 x = 24 - 2 y$ by $7$ and simplify.

Divide each term in $7 x = 24 - 2 y$ by $7$ .

$\frac{7 x}{7} = \frac{24}{7} + \frac{- 2 y}{7}$

$8 x + 2 y = 30$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{24}{7} + \frac{- 2 y}{7}$

$8 x + 2 y = 30$

Divide $x$ by $1$ .

$x = \frac{24}{7} + \frac{- 2 y}{7}$

$8 x + 2 y = 30$

$x = \frac{24}{7} + \frac{- 2 y}{7}$

$8 x + 2 y = 30$

$x = \frac{24}{7} + \frac{- 2 y}{7}$

$8 x + 2 y = 30$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{24}{7} - \frac{2 y}{7}$

$8 x + 2 y = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

$8 x + 2 y = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

$8 x + 2 y = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

$8 x + 2 y = 30$

Step 2

Replace all occurrences of $x$ with $\frac{24}{7} - \frac{2 y}{7}$ in each equation.

Replace all occurrences of $x$ in $8 x + 2 y = 30$ with $\frac{24}{7} - \frac{2 y}{7}$ .

$8 (\frac{24}{7} - \frac{2 y}{7}) + 2 y = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

Simplify the left side.

Simplify $8 (\frac{24}{7} - \frac{2 y}{7}) + 2 y$ .

Simplify each term.

Apply the distributive property.

$8 (\frac{24}{7}) + 8 (- \frac{2 y}{7}) + 2 y = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

Multiply $8 (\frac{24}{7})$ .

Combine $8$ and $\frac{24}{7}$ .

$\frac{8 \cdot 24}{7} + 8 (- \frac{2 y}{7}) + 2 y = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

Multiply $8$ by $24$ .

$\frac{192}{7} + 8 (- \frac{2 y}{7}) + 2 y = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

$\frac{192}{7} + 8 (- \frac{2 y}{7}) + 2 y = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

Multiply $8 (- \frac{2 y}{7})$ .

Multiply $- 1$ by $8$ .

$\frac{192}{7} - 8 \frac{2 y}{7} + 2 y = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

Combine $- 8$ and $\frac{2 y}{7}$ .

$\frac{192}{7} + \frac{- 8 (2 y)}{7} + 2 y = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

Multiply $2$ by $- 8$ .

$\frac{192}{7} + \frac{- 16 y}{7} + 2 y = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

$\frac{192}{7} + \frac{- 16 y}{7} + 2 y = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

Move the negative in front of the fraction.

$\frac{192}{7} - \frac{16 y}{7} + 2 y = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

$\frac{192}{7} - \frac{16 y}{7} + 2 y = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

To write $2 y$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{192}{7} - \frac{16 y}{7} + 2 y \cdot \frac{7}{7} = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

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

$\frac{192}{7} - \frac{16 y}{7} + \frac{2 y \cdot 7}{7} = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

Combine the numerators over the common denominator.

$\frac{192}{7} + \frac{- 16 y + 2 y \cdot 7}{7} = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

Combine the numerators over the common denominator.

$\frac{192 - 16 y + 2 y \cdot 7}{7} = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

Multiply $7$ by $2$ .

$\frac{192 - 16 y + 14 y}{7} = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

Add $- 16 y$ and $14 y$ .

$\frac{192 - 2 y}{7} = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

Factor $2$ out of $192 - 2 y$ .

Factor $2$ out of $192$ .

$\frac{2 (96) - 2 y}{7} = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

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

$\frac{2 (96) + 2 (- y)}{7} = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

Factor $2$ out of $2 (96) + 2 (- y)$ .

$\frac{2 (96 - y)}{7} = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

$\frac{2 (96 - y)}{7} = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

$\frac{2 (96 - y)}{7} = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

$\frac{2 (96 - y)}{7} = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

$\frac{2 (96 - y)}{7} = 30$

$x = \frac{24}{7} - \frac{2 y}{7}$

Step 3

Solve for $y$ in $\frac{2 (96 - y)}{7} = 30$ .

Multiply both sides by $7$ .

$\frac{2 (96 - y)}{7} \cdot 7 = 30 \cdot 7$

$x = \frac{24}{7} - \frac{2 y}{7}$

Simplify.

Simplify the left side.

Simplify $\frac{2 (96 - y)}{7} \cdot 7$ .

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{2 (96 - y)}{7} \cdot 7 = 30 \cdot 7$

$x = \frac{24}{7} - \frac{2 y}{7}$

Rewrite the expression.

$2 (96 - y) = 30 \cdot 7$

$x = \frac{24}{7} - \frac{2 y}{7}$

$2 (96 - y) = 30 \cdot 7$

$x = \frac{24}{7} - \frac{2 y}{7}$

Apply the distributive property.

$2 \cdot 96 + 2 (- y) = 30 \cdot 7$

$x = \frac{24}{7} - \frac{2 y}{7}$

Simplify the expression.

Multiply $2$ by $96$ .

$192 + 2 (- y) = 30 \cdot 7$

$x = \frac{24}{7} - \frac{2 y}{7}$

Multiply $- 1$ by $2$ .

$192 - 2 y = 30 \cdot 7$

$x = \frac{24}{7} - \frac{2 y}{7}$

Reorder $192$ and $- 2 y$ .

$- 2 y + 192 = 30 \cdot 7$

$x = \frac{24}{7} - \frac{2 y}{7}$

$- 2 y + 192 = 30 \cdot 7$

$x = \frac{24}{7} - \frac{2 y}{7}$

$- 2 y + 192 = 30 \cdot 7$

$x = \frac{24}{7} - \frac{2 y}{7}$

$- 2 y + 192 = 30 \cdot 7$

$x = \frac{24}{7} - \frac{2 y}{7}$

Simplify the right side.

Multiply $30$ by $7$ .

$- 2 y + 192 = 210$

$x = \frac{24}{7} - \frac{2 y}{7}$

$- 2 y + 192 = 210$

$x = \frac{24}{7} - \frac{2 y}{7}$

$- 2 y + 192 = 210$

$x = \frac{24}{7} - \frac{2 y}{7}$

Solve for $y$ .

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

Subtract $192$ from both sides of the equation.

$- 2 y = 210 - 192$

$x = \frac{24}{7} - \frac{2 y}{7}$

Subtract $192$ from $210$ .

$- 2 y = 18$

$x = \frac{24}{7} - \frac{2 y}{7}$

$- 2 y = 18$

$x = \frac{24}{7} - \frac{2 y}{7}$

Divide each term in $- 2 y = 18$ by $- 2$ and simplify.

Divide each term in $- 2 y = 18$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{18}{- 2}$

$x = \frac{24}{7} - \frac{2 y}{7}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{18}{- 2}$

$x = \frac{24}{7} - \frac{2 y}{7}$

Divide $y$ by $1$ .

$y = \frac{18}{- 2}$

$x = \frac{24}{7} - \frac{2 y}{7}$

$y = \frac{18}{- 2}$

$x = \frac{24}{7} - \frac{2 y}{7}$

$y = \frac{18}{- 2}$

$x = \frac{24}{7} - \frac{2 y}{7}$

Simplify the right side.

Divide $18$ by $- 2$ .

$y = - 9$

$x = \frac{24}{7} - \frac{2 y}{7}$

$y = - 9$

$x = \frac{24}{7} - \frac{2 y}{7}$

$y = - 9$

$x = \frac{24}{7} - \frac{2 y}{7}$

$y = - 9$

$x = \frac{24}{7} - \frac{2 y}{7}$

$y = - 9$

$x = \frac{24}{7} - \frac{2 y}{7}$

Step 4

Replace all occurrences of $y$ with $- 9$ in each equation.

Replace all occurrences of $y$ in $x = \frac{24}{7} - \frac{2 y}{7}$ with $- 9$ .

$x = \frac{24}{7} - \frac{2 (- 9)}{7}$

$y = - 9$

Simplify the right side.

Simplify $\frac{24}{7} - \frac{2 (- 9)}{7}$ .

Combine the numerators over the common denominator.

$x = \frac{24 - 2 \cdot - 9}{7}$

$y = - 9$

Simplify the expression.

Multiply $- 2$ by $- 9$ .

$x = \frac{24 + 18}{7}$

$y = - 9$

Add $24$ and $18$ .

$x = \frac{42}{7}$

$y = - 9$

Divide $42$ by $7$ .

$x = 6$

$y = - 9$

$x = 6$

$y = - 9$

$x = 6$

$y = - 9$

$x = 6$

$y = - 9$

$x = 6$

$y = - 9$

Step 5

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

$(6, - 9)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(6, - 9)$

Equation Form:

$x = 6, y = - 9$

Step 7

Solve by Substitution 7x+2y=24 , 8x+2y=30

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