Solve by Substitution -6x+6y=6 , -6x+3y=-12

$- 6 x + 6 y = 6$ , $- 6 x + 3 y = - 12$

Step 1

Solve for $x$ in $- 6 x + 6 y = 6$ .

Subtract $6 y$ from both sides of the equation.

$- 6 x = 6 - 6 y$

$- 6 x + 3 y = - 12$

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

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

$\frac{- 6 x}{- 6} = \frac{6}{- 6} + \frac{- 6 y}{- 6}$

$- 6 x + 3 y = - 12$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{6}{- 6} + \frac{- 6 y}{- 6}$

$- 6 x + 3 y = - 12$

Divide $x$ by $1$ .

$x = \frac{6}{- 6} + \frac{- 6 y}{- 6}$

$- 6 x + 3 y = - 12$

$x = \frac{6}{- 6} + \frac{- 6 y}{- 6}$

$- 6 x + 3 y = - 12$

$x = \frac{6}{- 6} + \frac{- 6 y}{- 6}$

$- 6 x + 3 y = - 12$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 6$ .

$x = - 1 + \frac{- 6 y}{- 6}$

$- 6 x + 3 y = - 12$

Cancel the common factor of $- 6$ .

Cancel the common factor.

$x = - 1 + \frac{- 6 y}{- 6}$

$- 6 x + 3 y = - 12$

Divide $y$ by $1$ .

$x = - 1 + y$

$- 6 x + 3 y = - 12$

$x = - 1 + y$

$- 6 x + 3 y = - 12$

$x = - 1 + y$

$- 6 x + 3 y = - 12$

$x = - 1 + y$

$- 6 x + 3 y = - 12$

$x = - 1 + y$

$- 6 x + 3 y = - 12$

$x = - 1 + y$

$- 6 x + 3 y = - 12$

Step 2

Replace all occurrences of $x$ with $- 1 + y$ in each equation.

Replace all occurrences of $x$ in $- 6 x + 3 y = - 12$ with $- 1 + y$ .

$- 6 (- 1 + y) + 3 y = - 12$

$x = - 1 + y$

Simplify the left side.

Simplify $- 6 (- 1 + y) + 3 y$ .

Simplify each term.

Apply the distributive property.

$- 6 \cdot - 1 - 6 y + 3 y = - 12$

$x = - 1 + y$

Multiply $- 6$ by $- 1$ .

$6 - 6 y + 3 y = - 12$

$x = - 1 + y$

$6 - 6 y + 3 y = - 12$

$x = - 1 + y$

Add $- 6 y$ and $3 y$ .

$6 - 3 y = - 12$

$x = - 1 + y$

$6 - 3 y = - 12$

$x = - 1 + y$

$6 - 3 y = - 12$

$x = - 1 + y$

$6 - 3 y = - 12$

$x = - 1 + y$

Step 3

Solve for $y$ in $6 - 3 y = - 12$ .

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

Subtract $6$ from both sides of the equation.

$- 3 y = - 12 - 6$

$x = - 1 + y$

Subtract $6$ from $- 12$ .

$- 3 y = - 18$

$x = - 1 + y$

$- 3 y = - 18$

$x = - 1 + y$

Divide each term in $- 3 y = - 18$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 18$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 18}{- 3}$

$x = - 1 + y$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 18}{- 3}$

$x = - 1 + y$

Divide $y$ by $1$ .

$y = \frac{- 18}{- 3}$

$x = - 1 + y$

$y = \frac{- 18}{- 3}$

$x = - 1 + y$

$y = \frac{- 18}{- 3}$

$x = - 1 + y$

Simplify the right side.

Divide $- 18$ by $- 3$ .

$y = 6$

$x = - 1 + y$

$y = 6$

$x = - 1 + y$

$y = 6$

$x = - 1 + y$

$y = 6$

$x = - 1 + y$

Step 4

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

Replace all occurrences of $y$ in $x = - 1 + y$ with $6$ .

$x = - 1 + 6$

$y = 6$

Simplify $x = - 1 + 6$ .

Simplify the left side.

Remove parentheses.

$x = - 1 + 6$

$y = 6$

$x = - 1 + 6$

$y = 6$

Simplify the right side.

Add $- 1$ and $6$ .

$x = 5$

$y = 6$

$x = 5$

$y = 6$

$x = 5$

$y = 6$

$x = 5$

$y = 6$

Step 5

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

$(5, 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(5, 6)$

Equation Form:

$x = 5, y = 6$

Step 7

Solve by Substitution -6x+6y=6 , -6x+3y=-12

Related Questions

Support LCMGCF.com by disabling your adblocker.