Solve by Substitution -4x-2y=-12 , 4x+8y=-24

$- 4 x - 2 y = - 12$ , $4 x + 8 y = - 24$

Step 1

Solve for $x$ in $- 4 x - 2 y = - 12$ .

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

$- 4 x = - 12 + 2 y$

$4 x + 8 y = - 24$

Divide each term in $- 4 x = - 12 + 2 y$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 12 + 2 y$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 12}{- 4} + \frac{2 y}{- 4}$

$4 x + 8 y = - 24$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 12}{- 4} + \frac{2 y}{- 4}$

$4 x + 8 y = - 24$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 4} + \frac{2 y}{- 4}$

$4 x + 8 y = - 24$

$x = \frac{- 12}{- 4} + \frac{2 y}{- 4}$

$4 x + 8 y = - 24$

$x = \frac{- 12}{- 4} + \frac{2 y}{- 4}$

$4 x + 8 y = - 24$

Simplify the right side.

Simplify each term.

Divide $- 12$ by $- 4$ .

$x = 3 + \frac{2 y}{- 4}$

$4 x + 8 y = - 24$

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

Factor $2$ out of $2 y$ .

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

$4 x + 8 y = - 24$

Cancel the common factors.

Factor $2$ out of $- 4$ .

$x = 3 + \frac{2 y}{2 \cdot - 2}$

$4 x + 8 y = - 24$

Cancel the common factor.

$x = 3 + \frac{2 y}{2 \cdot - 2}$

$4 x + 8 y = - 24$

Rewrite the expression.

$x = 3 + \frac{y}{- 2}$

$4 x + 8 y = - 24$

$x = 3 + \frac{y}{- 2}$

$4 x + 8 y = - 24$

$x = 3 + \frac{y}{- 2}$

$4 x + 8 y = - 24$

Move the negative in front of the fraction.

$x = 3 - \frac{y}{2}$

$4 x + 8 y = - 24$

$x = 3 - \frac{y}{2}$

$4 x + 8 y = - 24$

$x = 3 - \frac{y}{2}$

$4 x + 8 y = - 24$

$x = 3 - \frac{y}{2}$

$4 x + 8 y = - 24$

$x = 3 - \frac{y}{2}$

$4 x + 8 y = - 24$

Step 2

Replace all occurrences of $x$ with $3 - \frac{y}{2}$ in each equation.

Replace all occurrences of $x$ in $4 x + 8 y = - 24$ with $3 - \frac{y}{2}$ .

$4 (3 - \frac{y}{2}) + 8 y = - 24$

$x = 3 - \frac{y}{2}$

Simplify the left side.

Simplify $4 (3 - \frac{y}{2}) + 8 y$ .

Simplify each term.

Apply the distributive property.

$4 \cdot 3 + 4 (- \frac{y}{2}) + 8 y = - 24$

$x = 3 - \frac{y}{2}$

Multiply $4$ by $3$ .

$12 + 4 (- \frac{y}{2}) + 8 y = - 24$

$x = 3 - \frac{y}{2}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{y}{2}$ into the numerator.

$12 + 4 (\frac{- y}{2}) + 8 y = - 24$

$x = 3 - \frac{y}{2}$

Factor $2$ out of $4$ .

$12 + 2 (2) (\frac{- y}{2}) + 8 y = - 24$

$x = 3 - \frac{y}{2}$

Cancel the common factor.

$12 + 2 \cdot (2 (\frac{- y}{2})) + 8 y = - 24$

$x = 3 - \frac{y}{2}$

Rewrite the expression.

$12 + 2 (- y) + 8 y = - 24$

$x = 3 - \frac{y}{2}$

$12 + 2 (- y) + 8 y = - 24$

$x = 3 - \frac{y}{2}$

Multiply $- 1$ by $2$ .

$12 - 2 y + 8 y = - 24$

$x = 3 - \frac{y}{2}$

$12 - 2 y + 8 y = - 24$

$x = 3 - \frac{y}{2}$

Add $- 2 y$ and $8 y$ .

$12 + 6 y = - 24$

$x = 3 - \frac{y}{2}$

$12 + 6 y = - 24$

$x = 3 - \frac{y}{2}$

$12 + 6 y = - 24$

$x = 3 - \frac{y}{2}$

$12 + 6 y = - 24$

$x = 3 - \frac{y}{2}$

Step 3

Solve for $y$ in $12 + 6 y = - 24$ .

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

Subtract $12$ from both sides of the equation.

$6 y = - 24 - 12$

$x = 3 - \frac{y}{2}$

Subtract $12$ from $- 24$ .

$6 y = - 36$

$x = 3 - \frac{y}{2}$

$6 y = - 36$

$x = 3 - \frac{y}{2}$

Divide each term in $6 y = - 36$ by $6$ and simplify.

Divide each term in $6 y = - 36$ by $6$ .

$\frac{6 y}{6} = \frac{- 36}{6}$

$x = 3 - \frac{y}{2}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 36}{6}$

$x = 3 - \frac{y}{2}$

Divide $y$ by $1$ .

$y = \frac{- 36}{6}$

$x = 3 - \frac{y}{2}$

$y = \frac{- 36}{6}$

$x = 3 - \frac{y}{2}$

$y = \frac{- 36}{6}$

$x = 3 - \frac{y}{2}$

Simplify the right side.

Divide $- 36$ by $6$ .

$y = - 6$

$x = 3 - \frac{y}{2}$

$y = - 6$

$x = 3 - \frac{y}{2}$

$y = - 6$

$x = 3 - \frac{y}{2}$

$y = - 6$

$x = 3 - \frac{y}{2}$

Step 4

Replace all occurrences of $y$ with $- 6$ in each equation.

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

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

$y = - 6$

Simplify the right side.

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

Simplify each term.

Divide $- 6$ by $2$ .

$x = 3 + 3$

$y = - 6$

Multiply $- 1$ by $- 3$ .

$x = 3 + 3$

$y = - 6$

$x = 3 + 3$

$y = - 6$

Add $3$ and $3$ .

$x = 6$

$y = - 6$

$x = 6$

$y = - 6$

$x = 6$

$y = - 6$

$x = 6$

$y = - 6$

Step 5

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

$(6, - 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(6, - 6)$

Equation Form:

$x = 6, y = - 6$

Step 7

Solve by Substitution -4x-2y=-12 , 4x+8y=-24

Related Questions

Support LCMGCF.com by disabling your adblocker.