Solve by Substitution -2x+6y=6 , -7x+8y=-5

$- 2 x + 6 y = 6$ , $- 7 x + 8 y = - 5$

Step 1

Solve for $x$ in $- 2 x + 6 y = 6$ .

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

$- 2 x = 6 - 6 y$

$- 7 x + 8 y = - 5$

Divide each term in $- 2 x = 6 - 6 y$ by $- 2$ and simplify.

Divide each term in $- 2 x = 6 - 6 y$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{6}{- 2} + \frac{- 6 y}{- 2}$

$- 7 x + 8 y = - 5$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{6}{- 2} + \frac{- 6 y}{- 2}$

$- 7 x + 8 y = - 5$

Divide $x$ by $1$ .

$x = \frac{6}{- 2} + \frac{- 6 y}{- 2}$

$- 7 x + 8 y = - 5$

$x = \frac{6}{- 2} + \frac{- 6 y}{- 2}$

$- 7 x + 8 y = - 5$

$x = \frac{6}{- 2} + \frac{- 6 y}{- 2}$

$- 7 x + 8 y = - 5$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 2$ .

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

$- 7 x + 8 y = - 5$

Cancel the common factor of $- 6$ and $- 2$ .

Factor $- 2$ out of $- 6 y$ .

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

$- 7 x + 8 y = - 5$

Cancel the common factors.

Factor $- 2$ out of $- 2$ .

$x = - 3 + \frac{- 2 (3 y)}{- 2 \cdot 1}$

$- 7 x + 8 y = - 5$

Cancel the common factor.

$x = - 3 + \frac{- 2 (3 y)}{- 2 \cdot 1}$

$- 7 x + 8 y = - 5$

Rewrite the expression.

$x = - 3 + \frac{3 y}{1}$

$- 7 x + 8 y = - 5$

Divide $3 y$ by $1$ .

$x = - 3 + 3 y$

$- 7 x + 8 y = - 5$

$x = - 3 + 3 y$

$- 7 x + 8 y = - 5$

$x = - 3 + 3 y$

$- 7 x + 8 y = - 5$

$x = - 3 + 3 y$

$- 7 x + 8 y = - 5$

$x = - 3 + 3 y$

$- 7 x + 8 y = - 5$

$x = - 3 + 3 y$

$- 7 x + 8 y = - 5$

$x = - 3 + 3 y$

$- 7 x + 8 y = - 5$

Step 2

Replace all occurrences of $x$ with $- 3 + 3 y$ in each equation.

Replace all occurrences of $x$ in $- 7 x + 8 y = - 5$ with $- 3 + 3 y$ .

$- 7 (- 3 + 3 y) + 8 y = - 5$

$x = - 3 + 3 y$

Simplify the left side.

Simplify $- 7 (- 3 + 3 y) + 8 y$ .

Simplify each term.

Apply the distributive property.

$- 7 \cdot - 3 - 7 (3 y) + 8 y = - 5$

$x = - 3 + 3 y$

Multiply $- 7$ by $- 3$ .

$21 - 7 (3 y) + 8 y = - 5$

$x = - 3 + 3 y$

Multiply $3$ by $- 7$ .

$21 - 21 y + 8 y = - 5$

$x = - 3 + 3 y$

$21 - 21 y + 8 y = - 5$

$x = - 3 + 3 y$

Add $- 21 y$ and $8 y$ .

$21 - 13 y = - 5$

$x = - 3 + 3 y$

$21 - 13 y = - 5$

$x = - 3 + 3 y$

$21 - 13 y = - 5$

$x = - 3 + 3 y$

$21 - 13 y = - 5$

$x = - 3 + 3 y$

Step 3

Solve for $y$ in $21 - 13 y = - 5$ .

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

Subtract $21$ from both sides of the equation.

$- 13 y = - 5 - 21$

$x = - 3 + 3 y$

Subtract $21$ from $- 5$ .

$- 13 y = - 26$

$x = - 3 + 3 y$

$- 13 y = - 26$

$x = - 3 + 3 y$

Divide each term in $- 13 y = - 26$ by $- 13$ and simplify.

Divide each term in $- 13 y = - 26$ by $- 13$ .

$\frac{- 13 y}{- 13} = \frac{- 26}{- 13}$

$x = - 3 + 3 y$

Simplify the left side.

Cancel the common factor of $- 13$ .

Cancel the common factor.

$\frac{- 13 y}{- 13} = \frac{- 26}{- 13}$

$x = - 3 + 3 y$

Divide $y$ by $1$ .

$y = \frac{- 26}{- 13}$

$x = - 3 + 3 y$

$y = \frac{- 26}{- 13}$

$x = - 3 + 3 y$

$y = \frac{- 26}{- 13}$

$x = - 3 + 3 y$

Simplify the right side.

Divide $- 26$ by $- 13$ .

$y = 2$

$x = - 3 + 3 y$

$y = 2$

$x = - 3 + 3 y$

$y = 2$

$x = - 3 + 3 y$

$y = 2$

$x = - 3 + 3 y$

Step 4

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

Replace all occurrences of $y$ in $x = - 3 + 3 y$ with $2$ .

$x = - 3 + 3 (2)$

$y = 2$

Simplify the right side.

Simplify $- 3 + 3 (2)$ .

Multiply $3$ by $2$ .

$x = - 3 + 6$

$y = 2$

Add $- 3$ and $6$ .

$x = 3$

$y = 2$

$x = 3$

$y = 2$

$x = 3$

$y = 2$

$x = 3$

$y = 2$

Step 5

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

$(3, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, 2)$

Equation Form:

$x = 3, y = 2$

Step 7

Solve by Substitution -2x+6y=6 , -7x+8y=-5

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