Solve the System of Equations -4x+8y=40 and -2x+y=-10

$- 4 x + 8 y = 40$ and $- 2 x + y = - 10$

Step 1

Add $2 x$ to both sides of the equation.

$y = - 10 + 2 x$

$- 4 x + 8 y = 40$

Step 2

Replace all occurrences of $y$ with $- 10 + 2 x$ in each equation.

Replace all occurrences of $y$ in $- 4 x + 8 y = 40$ with $- 10 + 2 x$ .

$- 4 x + 8 (- 10 + 2 x) = 40$

$y = - 10 + 2 x$

Simplify the left side.

Simplify $- 4 x + 8 (- 10 + 2 x)$ .

Simplify each term.

Apply the distributive property.

$- 4 x + 8 \cdot - 10 + 8 (2 x) = 40$

$y = - 10 + 2 x$

Multiply $8$ by $- 10$ .

$- 4 x - 80 + 8 (2 x) = 40$

$y = - 10 + 2 x$

Multiply $2$ by $8$ .

$- 4 x - 80 + 16 x = 40$

$y = - 10 + 2 x$

$- 4 x - 80 + 16 x = 40$

$y = - 10 + 2 x$

Add $- 4 x$ and $16 x$ .

$12 x - 80 = 40$

$y = - 10 + 2 x$

$12 x - 80 = 40$

$y = - 10 + 2 x$

$12 x - 80 = 40$

$y = - 10 + 2 x$

$12 x - 80 = 40$

$y = - 10 + 2 x$

Step 3

Solve for $x$ in $12 x - 80 = 40$ .

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

Add $80$ to both sides of the equation.

$12 x = 40 + 80$

$y = - 10 + 2 x$

Add $40$ and $80$ .

$12 x = 120$

$y = - 10 + 2 x$

$12 x = 120$

$y = - 10 + 2 x$

Divide each term in $12 x = 120$ by $12$ and simplify.

Divide each term in $12 x = 120$ by $12$ .

$\frac{12 x}{12} = \frac{120}{12}$

$y = - 10 + 2 x$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{120}{12}$

$y = - 10 + 2 x$

Divide $x$ by $1$ .

$x = \frac{120}{12}$

$y = - 10 + 2 x$

$x = \frac{120}{12}$

$y = - 10 + 2 x$

$x = \frac{120}{12}$

$y = - 10 + 2 x$

Simplify the right side.

Divide $120$ by $12$ .

$x = 10$

$y = - 10 + 2 x$

$x = 10$

$y = - 10 + 2 x$

$x = 10$

$y = - 10 + 2 x$

$x = 10$

$y = - 10 + 2 x$

Step 4

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

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

$y = - 10 + 2 (10)$

$x = 10$

Simplify the right side.

Simplify $- 10 + 2 (10)$ .

Multiply $2$ by $10$ .

$y = - 10 + 20$

$x = 10$

Add $- 10$ and $20$ .

$y = 10$

$x = 10$

$y = 10$

$x = 10$

$y = 10$

$x = 10$

$y = 10$

$x = 10$

Step 5

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

$(10, 10)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(10, 10)$

Equation Form:

$x = 10, y = 10$

Step 7

Solve the System of Equations -4x+8y=40 and -2x+y=-10

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