Solve by Substitution -7x+4y=24 , 4x-4y=0

$- 7 x + 4 y = 24$ , $4 x - 4 y = 0$

Step 1

Solve for $x$ in $- 7 x + 4 y = 24$ .

Subtract $4 y$ from both sides of the equation.

$- 7 x = 24 - 4 y$

$4 x - 4 y = 0$

Divide each term in $- 7 x = 24 - 4 y$ by $- 7$ and simplify.

Divide each term in $- 7 x = 24 - 4 y$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{24}{- 7} + \frac{- 4 y}{- 7}$

$4 x - 4 y = 0$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{24}{- 7} + \frac{- 4 y}{- 7}$

$4 x - 4 y = 0$

Divide $x$ by $1$ .

$x = \frac{24}{- 7} + \frac{- 4 y}{- 7}$

$4 x - 4 y = 0$

$x = \frac{24}{- 7} + \frac{- 4 y}{- 7}$

$4 x - 4 y = 0$

$x = \frac{24}{- 7} + \frac{- 4 y}{- 7}$

$4 x - 4 y = 0$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{24}{7} + \frac{- 4 y}{- 7}$

$4 x - 4 y = 0$

Dividing two negative values results in a positive value.

$x = - \frac{24}{7} + \frac{4 y}{7}$

$4 x - 4 y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$4 x - 4 y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$4 x - 4 y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$4 x - 4 y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$4 x - 4 y = 0$

Step 2

Replace all occurrences of $x$ with $- \frac{24}{7} + \frac{4 y}{7}$ in each equation.

Replace all occurrences of $x$ in $4 x - 4 y = 0$ with $- \frac{24}{7} + \frac{4 y}{7}$ .

$4 (- \frac{24}{7} + \frac{4 y}{7}) - 4 y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Simplify the left side.

Simplify $4 (- \frac{24}{7} + \frac{4 y}{7}) - 4 y$ .

Simplify each term.

Apply the distributive property.

$4 (- \frac{24}{7}) + 4 (\frac{4 y}{7}) - 4 y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Multiply $4 (- \frac{24}{7})$ .

Multiply $- 1$ by $4$ .

$- 4 (\frac{24}{7}) + 4 (\frac{4 y}{7}) - 4 y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Combine $- 4$ and $\frac{24}{7}$ .

$\frac{- 4 \cdot 24}{7} + 4 (\frac{4 y}{7}) - 4 y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Multiply $- 4$ by $24$ .

$\frac{- 96}{7} + 4 (\frac{4 y}{7}) - 4 y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$\frac{- 96}{7} + 4 (\frac{4 y}{7}) - 4 y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Multiply $4 \frac{4 y}{7}$ .

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

$\frac{- 96}{7} + \frac{4 (4 y)}{7} - 4 y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Multiply $4$ by $4$ .

$\frac{- 96}{7} + \frac{16 y}{7} - 4 y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$\frac{- 96}{7} + \frac{16 y}{7} - 4 y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Move the negative in front of the fraction.

$- \frac{96}{7} + \frac{16 y}{7} - 4 y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$- \frac{96}{7} + \frac{16 y}{7} - 4 y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

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

$- \frac{96}{7} + \frac{16 y}{7} - 4 y \cdot \frac{7}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

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

$- \frac{96}{7} + \frac{16 y}{7} + \frac{- 4 y \cdot 7}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Combine the numerators over the common denominator.

$- \frac{96}{7} + \frac{16 y - 4 y \cdot 7}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Combine the numerators over the common denominator.

$\frac{- 96 + 16 y - 4 y \cdot 7}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Multiply $7$ by $- 4$ .

$\frac{- 96 + 16 y - 28 y}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Subtract $28 y$ from $16 y$ .

$\frac{- 96 - 12 y}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Factor $12$ out of $- 96 - 12 y$ .

Factor $12$ out of $- 96$ .

$\frac{12 (- 8) - 12 y}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Factor $12$ out of $- 12 y$ .

$\frac{12 (- 8) + 12 (- y)}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Factor $12$ out of $12 (- 8) + 12 (- y)$ .

$\frac{12 (- 8 - y)}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$\frac{12 (- 8 - y)}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Rewrite $- 8$ as $- 1 (8)$ .

$\frac{12 (- 1 \cdot 8 - y)}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Factor $- 1$ out of $- y$ .

$\frac{12 (- 1 \cdot 8 - (y))}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Factor $- 1$ out of $- 1 (8) - (y)$ .

$\frac{12 (- 1 (8 + y))}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Move the negative in front of the fraction.

$- \frac{12 (8 + y)}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$- \frac{12 (8 + y)}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$- \frac{12 (8 + y)}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$- \frac{12 (8 + y)}{7} = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Step 3

Solve for $y$ in $- \frac{12 (8 + y)}{7} = 0$ .

Set the numerator equal to zero.

$12 (8 + y) = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Solve the equation for $y$ .

Divide each term in $12 (8 + y) = 0$ by $12$ and simplify.

Divide each term in $12 (8 + y) = 0$ by $12$ .

$\frac{12 (8 + y)}{12} = \frac{0}{12}$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 (8 + y)}{12} = \frac{0}{12}$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Divide $8 + y$ by $1$ .

$8 + y = \frac{0}{12}$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$8 + y = \frac{0}{12}$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$8 + y = \frac{0}{12}$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Simplify the right side.

Divide $0$ by $12$ .

$8 + y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$8 + y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$8 + y = 0$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Subtract $8$ from both sides of the equation.

$y = - 8$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$y = - 8$

$x = - \frac{24}{7} + \frac{4 y}{7}$

$y = - 8$

$x = - \frac{24}{7} + \frac{4 y}{7}$

Step 4

Replace all occurrences of $y$ with $- 8$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{24}{7} + \frac{4 y}{7}$ with $- 8$ .

$x = - \frac{24}{7} + \frac{4 (- 8)}{7}$

$y = - 8$

Simplify the right side.

Simplify $- \frac{24}{7} + \frac{4 (- 8)}{7}$ .

Combine the numerators over the common denominator.

$x = \frac{- 24 + 4 (- 8)}{7}$

$y = - 8$

Simplify the expression.

Multiply $4$ by $- 8$ .

$x = \frac{- 24 - 32}{7}$

$y = - 8$

Subtract $32$ from $- 24$ .

$x = \frac{- 56}{7}$

$y = - 8$

Divide $- 56$ by $7$ .

$x = - 8$

$y = - 8$

$x = - 8$

$y = - 8$

$x = - 8$

$y = - 8$

$x = - 8$

$y = - 8$

$x = - 8$

$y = - 8$

Step 5

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

$(- 8, - 8)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 8, - 8)$

Equation Form:

$x = - 8, y = - 8$

Step 7

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