Solve the System of Equations x-3y=-14 and -3x-7y=10

$x - 3 y = - 14$ and $- 3 x - 7 y = 10$

Add $3 y$ to both sides of the equation.

$x = - 14 + 3 y$

$- 3 x - 7 y = 10$

Replace all occurrences of $x$ with $- 14 + 3 y$ in each equation.

Replace all occurrences of $x$ in $- 3 x - 7 y = 10$ with $- 14 + 3 y$ .

$- 3 (- 14 + 3 y) - 7 y = 10$

$x = - 14 + 3 y$

Simplify the left side.

Simplify $- 3 (- 14 + 3 y) - 7 y$ .

Simplify each term.

Apply the distributive property.

$- 3 \cdot - 14 - 3 (3 y) - 7 y = 10$

$x = - 14 + 3 y$

Multiply $- 3$ by $- 14$ .

$42 - 3 (3 y) - 7 y = 10$

$x = - 14 + 3 y$

Multiply $3$ by $- 3$ .

$42 - 9 y - 7 y = 10$

$x = - 14 + 3 y$

$42 - 9 y - 7 y = 10$

$x = - 14 + 3 y$

Subtract $7 y$ from $- 9 y$ .

$42 - 16 y = 10$

$x = - 14 + 3 y$

$42 - 16 y = 10$

$x = - 14 + 3 y$

$42 - 16 y = 10$

$x = - 14 + 3 y$

$42 - 16 y = 10$

$x = - 14 + 3 y$

Solve for $y$ in $42 - 16 y = 10$ .

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

Subtract $42$ from both sides of the equation.

$- 16 y = 10 - 42$

$x = - 14 + 3 y$

Subtract $42$ from $10$ .

$- 16 y = - 32$

$x = - 14 + 3 y$

$- 16 y = - 32$

$x = - 14 + 3 y$

Divide each term in $- 16 y = - 32$ by $- 16$ and simplify.

Divide each term in $- 16 y = - 32$ by $- 16$ .

$\frac{- 16 y}{- 16} = \frac{- 32}{- 16}$

$x = - 14 + 3 y$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 y}{- 16} = \frac{- 32}{- 16}$

$x = - 14 + 3 y$

Divide $y$ by $1$ .

$y = \frac{- 32}{- 16}$

$x = - 14 + 3 y$

$y = \frac{- 32}{- 16}$

$x = - 14 + 3 y$

$y = \frac{- 32}{- 16}$

$x = - 14 + 3 y$

Simplify the right side.

Divide $- 32$ by $- 16$ .

$y = 2$

$x = - 14 + 3 y$

$y = 2$

$x = - 14 + 3 y$

$y = 2$

$x = - 14 + 3 y$

$y = 2$

$x = - 14 + 3 y$

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

Replace all occurrences of $y$ in $x = - 14 + 3 y$ with $2$ .

$x = - 14 + 3 (2)$

$y = 2$

Simplify the right side.

Simplify $- 14 + 3 (2)$ .

Multiply $3$ by $2$ .

$x = - 14 + 6$

$y = 2$

Add $- 14$ and $6$ .

$x = - 8$

$y = 2$

$x = - 8$

$y = 2$

$x = - 8$

$y = 2$

$x = - 8$

$y = 2$

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

$(- 8, 2)$

The result can be shown in multiple forms.

Point Form:

$(- 8, 2)$

Equation Form:

$x = - 8, y = 2$

Solve the System of Equations x-3y=-14 and -3x-7y=10

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