Solve the System of Equations 5x+7y=6 -10x-14y=-12

$5 x + 7 y = 6$ $- 10 x - 14 y = - 12$

Step 1

Solve for $x$ in $5 x + 7 y = 6$ .

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

$5 x = 6 - 7 y$

$- 10 x - 14 y = - 12$

Divide each term in $5 x = 6 - 7 y$ by $5$ and simplify.

Divide each term in $5 x = 6 - 7 y$ by $5$ .

$\frac{5 x}{5} = \frac{6}{5} + \frac{- 7 y}{5}$

$- 10 x - 14 y = - 12$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{6}{5} + \frac{- 7 y}{5}$

$- 10 x - 14 y = - 12$

Divide $x$ by $1$ .

$x = \frac{6}{5} + \frac{- 7 y}{5}$

$- 10 x - 14 y = - 12$

$x = \frac{6}{5} + \frac{- 7 y}{5}$

$- 10 x - 14 y = - 12$

$x = \frac{6}{5} + \frac{- 7 y}{5}$

$- 10 x - 14 y = - 12$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{6}{5} - \frac{7 y}{5}$

$- 10 x - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

$- 10 x - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

$- 10 x - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

$- 10 x - 14 y = - 12$

Step 2

Replace all occurrences of $x$ with $\frac{6}{5} - \frac{7 y}{5}$ in each equation.

Replace all occurrences of $x$ in $- 10 x - 14 y = - 12$ with $\frac{6}{5} - \frac{7 y}{5}$ .

$- 10 (\frac{6}{5} - \frac{7 y}{5}) - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

Simplify the left side.

Simplify $- 10 (\frac{6}{5} - \frac{7 y}{5}) - 14 y$ .

Simplify each term.

Apply the distributive property.

$- 10 (\frac{6}{5}) - 10 (- \frac{7 y}{5}) - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

Cancel the common factor of $5$ .

Factor $5$ out of $- 10$ .

$5 (- 2) (\frac{6}{5}) - 10 (- \frac{7 y}{5}) - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

Cancel the common factor.

$5 \cdot (- 2 (\frac{6}{5})) - 10 (- \frac{7 y}{5}) - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

Rewrite the expression.

$- 2 \cdot 6 - 10 (- \frac{7 y}{5}) - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

$- 2 \cdot 6 - 10 (- \frac{7 y}{5}) - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

Multiply $- 2$ by $6$ .

$- 12 - 10 (- \frac{7 y}{5}) - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{7 y}{5}$ into the numerator.

$- 12 - 10 \frac{- 7 y}{5} - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

Factor $5$ out of $- 10$ .

$- 12 + 5 (- 2) (\frac{- 7 y}{5}) - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

Cancel the common factor.

$- 12 + 5 \cdot (- 2 \frac{- 7 y}{5}) - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

Rewrite the expression.

$- 12 - 2 (- 7 y) - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

$- 12 - 2 (- 7 y) - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

Multiply $- 7$ by $- 2$ .

$- 12 + 14 y - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

$- 12 + 14 y - 14 y = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

Combine the opposite terms in $- 12 + 14 y - 14 y$ .

Subtract $14 y$ from $14 y$ .

$- 12 + 0 = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

Add $- 12$ and $0$ .

$- 12 = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

$- 12 = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

$- 12 = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

$- 12 = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

$- 12 = - 12$

$x = \frac{6}{5} - \frac{7 y}{5}$

Step 3

Remove any equations from the system that are always true.

$x = \frac{6}{5} - \frac{7 y}{5}$

Step 4

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