Solve the System of Equations -x+7y=12 and 6x-8y=-4

$- x + 7 y = 12$ and $6 x - 8 y = - 4$

Step 1

Solve for $x$ in $- x + 7 y = 12$ .

Subtract $7 y$ from both sides of the equation.

$- x = 12 - 7 y$

$6 x - 8 y = - 4$

Divide each term in $- x = 12 - 7 y$ by $- 1$ and simplify.

Divide each term in $- x = 12 - 7 y$ by $- 1$ .

$\frac{- x}{- 1} = \frac{12}{- 1} + \frac{- 7 y}{- 1}$

$6 x - 8 y = - 4$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{12}{- 1} + \frac{- 7 y}{- 1}$

$6 x - 8 y = - 4$

Divide $x$ by $1$ .

$x = \frac{12}{- 1} + \frac{- 7 y}{- 1}$

$6 x - 8 y = - 4$

$x = \frac{12}{- 1} + \frac{- 7 y}{- 1}$

$6 x - 8 y = - 4$

Simplify the right side.

Simplify each term.

Divide $12$ by $- 1$ .

$x = - 12 + \frac{- 7 y}{- 1}$

$6 x - 8 y = - 4$

Move the negative one from the denominator of $\frac{- 7 y}{- 1}$ .

$x = - 12 - 1 \cdot (- 7 y)$

$6 x - 8 y = - 4$

Rewrite $- 1 \cdot (- 7 y)$ as $- (- 7 y)$ .

$x = - 12 - (- 7 y)$

$6 x - 8 y = - 4$

Multiply $- 7$ by $- 1$ .

$x = - 12 + 7 y$

$6 x - 8 y = - 4$

$x = - 12 + 7 y$

$6 x - 8 y = - 4$

$x = - 12 + 7 y$

$6 x - 8 y = - 4$

$x = - 12 + 7 y$

$6 x - 8 y = - 4$

$x = - 12 + 7 y$

$6 x - 8 y = - 4$

Step 2

Replace all occurrences of $x$ with $- 12 + 7 y$ in each equation.

Replace all occurrences of $x$ in $6 x - 8 y = - 4$ with $- 12 + 7 y$ .

$6 (- 12 + 7 y) - 8 y = - 4$

$x = - 12 + 7 y$

Simplify the left side.

Simplify $6 (- 12 + 7 y) - 8 y$ .

Simplify each term.

Apply the distributive property.

$6 \cdot - 12 + 6 (7 y) - 8 y = - 4$

$x = - 12 + 7 y$

Multiply $6$ by $- 12$ .

$- 72 + 6 (7 y) - 8 y = - 4$

$x = - 12 + 7 y$

Multiply $7$ by $6$ .

$- 72 + 42 y - 8 y = - 4$

$x = - 12 + 7 y$

$- 72 + 42 y - 8 y = - 4$

$x = - 12 + 7 y$

Subtract $8 y$ from $42 y$ .

$- 72 + 34 y = - 4$

$x = - 12 + 7 y$

$- 72 + 34 y = - 4$

$x = - 12 + 7 y$

$- 72 + 34 y = - 4$

$x = - 12 + 7 y$

$- 72 + 34 y = - 4$

$x = - 12 + 7 y$

Step 3

Solve for $y$ in $- 72 + 34 y = - 4$ .

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

Add $72$ to both sides of the equation.

$34 y = - 4 + 72$

$x = - 12 + 7 y$

Add $- 4$ and $72$ .

$34 y = 68$

$x = - 12 + 7 y$

$34 y = 68$

$x = - 12 + 7 y$

Divide each term in $34 y = 68$ by $34$ and simplify.

Divide each term in $34 y = 68$ by $34$ .

$\frac{34 y}{34} = \frac{68}{34}$

$x = - 12 + 7 y$

Simplify the left side.

Cancel the common factor of $34$ .

Cancel the common factor.

$\frac{34 y}{34} = \frac{68}{34}$

$x = - 12 + 7 y$

Divide $y$ by $1$ .

$y = \frac{68}{34}$

$x = - 12 + 7 y$

$y = \frac{68}{34}$

$x = - 12 + 7 y$

$y = \frac{68}{34}$

$x = - 12 + 7 y$

Simplify the right side.

Divide $68$ by $34$ .

$y = 2$

$x = - 12 + 7 y$

$y = 2$

$x = - 12 + 7 y$

$y = 2$

$x = - 12 + 7 y$

$y = 2$

$x = - 12 + 7 y$

Step 4

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

Replace all occurrences of $y$ in $x = - 12 + 7 y$ with $2$ .

$x = - 12 + 7 (2)$

$y = 2$

Simplify the right side.

Simplify $- 12 + 7 (2)$ .

Multiply $7$ by $2$ .

$x = - 12 + 14$

$y = 2$

Add $- 12$ and $14$ .

$x = 2$

$y = 2$

$x = 2$

$y = 2$

$x = 2$

$y = 2$

$x = 2$

$y = 2$

Step 5

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

$(2, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, 2)$

Equation Form:

$x = 2, y = 2$

Step 7

Solve the System of Equations -x+7y=12 and 6x-8y=-4

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