Solve the System of Equations -3x+7y=-18 and 4x-4y=8

$- 3 x + 7 y = - 18$ and $4 x - 4 y = 8$

Solve for $x$ in $- 3 x + 7 y = - 18$ .

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

$- 3 x = - 18 - 7 y$

$4 x - 4 y = 8$

Divide each term in $- 3 x = - 18 - 7 y$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 18 - 7 y$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 18}{- 3} + \frac{- 7 y}{- 3}$

$4 x - 4 y = 8$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 18}{- 3} + \frac{- 7 y}{- 3}$

$4 x - 4 y = 8$

Divide $x$ by $1$ .

$x = \frac{- 18}{- 3} + \frac{- 7 y}{- 3}$

$4 x - 4 y = 8$

$x = \frac{- 18}{- 3} + \frac{- 7 y}{- 3}$

$4 x - 4 y = 8$

$x = \frac{- 18}{- 3} + \frac{- 7 y}{- 3}$

$4 x - 4 y = 8$

Simplify the right side.

Simplify each term.

Divide $- 18$ by $- 3$ .

$x = 6 + \frac{- 7 y}{- 3}$

$4 x - 4 y = 8$

Dividing two negative values results in a positive value.

$x = 6 + \frac{7 y}{3}$

$4 x - 4 y = 8$

$x = 6 + \frac{7 y}{3}$

$4 x - 4 y = 8$

$x = 6 + \frac{7 y}{3}$

$4 x - 4 y = 8$

$x = 6 + \frac{7 y}{3}$

$4 x - 4 y = 8$

$x = 6 + \frac{7 y}{3}$

$4 x - 4 y = 8$

Replace all occurrences of $x$ with $6 + \frac{7 y}{3}$ in each equation.

Replace all occurrences of $x$ in $4 x - 4 y = 8$ with $6 + \frac{7 y}{3}$ .

$4 (6 + \frac{7 y}{3}) - 4 y = 8$

$x = 6 + \frac{7 y}{3}$

Simplify the left side.

Simplify $4 (6 + \frac{7 y}{3}) - 4 y$ .

Simplify each term.

Apply the distributive property.

$4 \cdot 6 + 4 (\frac{7 y}{3}) - 4 y = 8$

$x = 6 + \frac{7 y}{3}$

Multiply $4$ by $6$ .

$24 + 4 (\frac{7 y}{3}) - 4 y = 8$

$x = 6 + \frac{7 y}{3}$

Multiply $4 \frac{7 y}{3}$ .

Combine $4$ and $\frac{7 y}{3}$ .

$24 + \frac{4 (7 y)}{3} - 4 y = 8$

$x = 6 + \frac{7 y}{3}$

Multiply $7$ by $4$ .

$24 + \frac{28 y}{3} - 4 y = 8$

$x = 6 + \frac{7 y}{3}$

$24 + \frac{28 y}{3} - 4 y = 8$

$x = 6 + \frac{7 y}{3}$

$24 + \frac{28 y}{3} - 4 y = 8$

$x = 6 + \frac{7 y}{3}$

To write $- 4 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$24 + \frac{28 y}{3} - 4 y \cdot \frac{3}{3} = 8$

$x = 6 + \frac{7 y}{3}$

Simplify terms.

Combine $- 4 y$ and $\frac{3}{3}$ .

$24 + \frac{28 y}{3} + \frac{- 4 y \cdot 3}{3} = 8$

$x = 6 + \frac{7 y}{3}$

Combine the numerators over the common denominator.

$24 + \frac{28 y - 4 y \cdot 3}{3} = 8$

$x = 6 + \frac{7 y}{3}$

$24 + \frac{28 y - 4 y \cdot 3}{3} = 8$

$x = 6 + \frac{7 y}{3}$

Simplify the numerator.

Factor $4 y$ out of $28 y - 4 y \cdot 3$ .

Factor $4 y$ out of $28 y$ .

$24 + \frac{4 y (7) - 4 y \cdot 3}{3} = 8$

$x = 6 + \frac{7 y}{3}$

Factor $4 y$ out of $- 4 y \cdot 3$ .

$24 + \frac{4 y (7) + 4 y (- 1 \cdot 3)}{3} = 8$

$x = 6 + \frac{7 y}{3}$

Factor $4 y$ out of $4 y (7) + 4 y (- 1 \cdot 3)$ .

$24 + \frac{4 y (7 - 1 \cdot 3)}{3} = 8$

$x = 6 + \frac{7 y}{3}$

$24 + \frac{4 y (7 - 1 \cdot 3)}{3} = 8$

$x = 6 + \frac{7 y}{3}$

Multiply $- 1$ by $3$ .

$24 + \frac{4 y (7 - 3)}{3} = 8$

$x = 6 + \frac{7 y}{3}$

Subtract $3$ from $7$ .

$24 + \frac{4 y \cdot 4}{3} = 8$

$x = 6 + \frac{7 y}{3}$

Multiply $4$ by $4$ .

$24 + \frac{16 y}{3} = 8$

$x = 6 + \frac{7 y}{3}$

$24 + \frac{16 y}{3} = 8$

$x = 6 + \frac{7 y}{3}$

$24 + \frac{16 y}{3} = 8$

$x = 6 + \frac{7 y}{3}$

$24 + \frac{16 y}{3} = 8$

$x = 6 + \frac{7 y}{3}$

$24 + \frac{16 y}{3} = 8$

$x = 6 + \frac{7 y}{3}$

Solve for $y$ in $24 + \frac{16 y}{3} = 8$ .

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

Subtract $24$ from both sides of the equation.

$\frac{16 y}{3} = 8 - 24$

$x = 6 + \frac{7 y}{3}$

Subtract $24$ from $8$ .

$\frac{16 y}{3} = - 16$

$x = 6 + \frac{7 y}{3}$

$\frac{16 y}{3} = - 16$

$x = 6 + \frac{7 y}{3}$

Multiply both sides of the equation by $\frac{3}{16}$ .

$\frac{3}{16} \cdot \frac{16 y}{3} = \frac{3}{16} \cdot - 16$

$x = 6 + \frac{7 y}{3}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{16} \cdot \frac{16 y}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{16} \cdot \frac{16 y}{3} = \frac{3}{16} \cdot - 16$

$x = 6 + \frac{7 y}{3}$

Rewrite the expression.

$\frac{1}{16} \cdot (16 y) = \frac{3}{16} \cdot - 16$

$x = 6 + \frac{7 y}{3}$

$\frac{1}{16} \cdot (16 y) = \frac{3}{16} \cdot - 16$

$x = 6 + \frac{7 y}{3}$

Cancel the common factor of $16$ .

Factor $16$ out of $16 y$ .

$\frac{1}{16} \cdot (16 (y)) = \frac{3}{16} \cdot - 16$

$x = 6 + \frac{7 y}{3}$

Cancel the common factor.

$\frac{1}{16} \cdot (16 y) = \frac{3}{16} \cdot - 16$

$x = 6 + \frac{7 y}{3}$

Rewrite the expression.

$y = \frac{3}{16} \cdot - 16$

$x = 6 + \frac{7 y}{3}$

$y = \frac{3}{16} \cdot - 16$

$x = 6 + \frac{7 y}{3}$

$y = \frac{3}{16} \cdot - 16$

$x = 6 + \frac{7 y}{3}$

$y = \frac{3}{16} \cdot - 16$

$x = 6 + \frac{7 y}{3}$

Simplify the right side.

Simplify $\frac{3}{16} \cdot - 16$ .

Cancel the common factor of $16$ .

Factor $16$ out of $- 16$ .

$y = \frac{3}{16} \cdot (16 (- 1))$

$x = 6 + \frac{7 y}{3}$

Cancel the common factor.

$y = \frac{3}{16} \cdot (16 \cdot - 1)$

$x = 6 + \frac{7 y}{3}$

Rewrite the expression.

$y = 3 \cdot - 1$

$x = 6 + \frac{7 y}{3}$

$y = 3 \cdot - 1$

$x = 6 + \frac{7 y}{3}$

Multiply $3$ by $- 1$ .

$y = - 3$

$x = 6 + \frac{7 y}{3}$

$y = - 3$

$x = 6 + \frac{7 y}{3}$

$y = - 3$

$x = 6 + \frac{7 y}{3}$

$y = - 3$

$x = 6 + \frac{7 y}{3}$

$y = - 3$

$x = 6 + \frac{7 y}{3}$

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

Replace all occurrences of $y$ in $x = 6 + \frac{7 y}{3}$ with $- 3$ .

$x = 6 + \frac{7 (- 3)}{3}$

$y = - 3$

Simplify the right side.

Simplify $6 + \frac{7 (- 3)}{3}$ .

Multiply $7$ by $- 3$ .

$x = 6 + \frac{- 21}{3}$

$y = - 3$

Divide $- 21$ by $3$ .

$x = 6 - 7$

$y = - 3$

Subtract $7$ from $6$ .

$x = - 1$

$y = - 3$

$x = - 1$

$y = - 3$

$x = - 1$

$y = - 3$

$x = - 1$

$y = - 3$

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

$(- 1, - 3)$

The result can be shown in multiple forms.

Point Form:

$(- 1, - 3)$

Equation Form:

$x = - 1, y = - 3$

Solve the System of Equations -3x+7y=-18 and 4x-4y=8

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