Solve the System of Equations -2y=4x-4 and 7x=-4y+10

$- 2 y = 4 x - 4$ and $7 x = - 4 y + 10$

Step 1

Divide each term in $- 2 y = 4 x - 4$ by $- 2$ and simplify.

Divide each term in $- 2 y = 4 x - 4$ by $- 2$ .

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

$7 x = - 4 y + 10$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$7 x = - 4 y + 10$

Divide $y$ by $1$ .

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

$7 x = - 4 y + 10$

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

$7 x = - 4 y + 10$

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

$7 x = - 4 y + 10$

Simplify the right side.

Simplify each term.

Cancel the common factor of $4$ and $- 2$ .

Factor $2$ out of $4 x$ .

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

$7 x = - 4 y + 10$

Move the negative one from the denominator of $\frac{2 x}{- 1}$ .

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

$7 x = - 4 y + 10$

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

$7 x = - 4 y + 10$

Rewrite $- 1 \cdot (2 x)$ as $- (2 x)$ .

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

$7 x = - 4 y + 10$

Multiply $2$ by $- 1$ .

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

$7 x = - 4 y + 10$

Divide $- 4$ by $- 2$ .

$y = - 2 x + 2$

$7 x = - 4 y + 10$

$y = - 2 x + 2$

$7 x = - 4 y + 10$

$y = - 2 x + 2$

$7 x = - 4 y + 10$

$y = - 2 x + 2$

$7 x = - 4 y + 10$

Step 2

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

Replace all occurrences of $y$ in $7 x = - 4 y + 10$ with $- 2 x + 2$ .

$7 x = - 4 (- 2 x + 2) + 10$

$y = - 2 x + 2$

Simplify the right side.

Simplify $- 4 (- 2 x + 2) + 10$ .

Simplify each term.

Apply the distributive property.

$7 x = - 4 (- 2 x) - 4 \cdot 2 + 10$

$y = - 2 x + 2$

Multiply $- 2$ by $- 4$ .

$7 x = 8 x - 4 \cdot 2 + 10$

$y = - 2 x + 2$

Multiply $- 4$ by $2$ .

$7 x = 8 x - 8 + 10$

$y = - 2 x + 2$

$7 x = 8 x - 8 + 10$

$y = - 2 x + 2$

Add $- 8$ and $10$ .

$7 x = 8 x + 2$

$y = - 2 x + 2$

$7 x = 8 x + 2$

$y = - 2 x + 2$

$7 x = 8 x + 2$

$y = - 2 x + 2$

$7 x = 8 x + 2$

$y = - 2 x + 2$

Step 3

Solve for $x$ in $7 x = 8 x + 2$ .

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

Subtract $8 x$ from both sides of the equation.

$7 x - 8 x = 2$

$y = - 2 x + 2$

Subtract $8 x$ from $7 x$ .

$- x = 2$

$y = - 2 x + 2$

$- x = 2$

$y = - 2 x + 2$

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

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

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

$y = - 2 x + 2$

Simplify the left side.

Dividing two negative values results in a positive value.

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

$y = - 2 x + 2$

Divide $x$ by $1$ .

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

$y = - 2 x + 2$

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

$y = - 2 x + 2$

Simplify the right side.

Divide $2$ by $- 1$ .

$x = - 2$

$y = - 2 x + 2$

$x = - 2$

$y = - 2 x + 2$

$x = - 2$

$y = - 2 x + 2$

$x = - 2$

$y = - 2 x + 2$

Step 4

Replace all occurrences of $x$ with $- 2$ in each equation.

Replace all occurrences of $x$ in $y = - 2 x + 2$ with $- 2$ .

$y = - 2 \cdot - 2 + 2$

$x = - 2$

Simplify the right side.

Simplify $- 2 \cdot - 2 + 2$ .

Multiply $- 2$ by $- 2$ .

$y = 4 + 2$

$x = - 2$

Add $4$ and $2$ .

$y = 6$

$x = - 2$

$y = 6$

$x = - 2$

$y = 6$

$x = - 2$

$y = 6$

$x = - 2$

Step 5

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

$(- 2, 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 2, 6)$

Equation Form:

$x = - 2, y = 6$

Step 7

Solve the System of Equations -2y=4x-4 and 7x=-4y+10

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