Solve by Substitution -7x+2y=18 , 6x+6y=0

$- 7 x + 2 y = 18$ , $6 x + 6 y = 0$

Step 1

Solve for $x$ in $- 7 x + 2 y = 18$ .

Subtract $2 y$ from both sides of the equation.

$- 7 x = 18 - 2 y$

$6 x + 6 y = 0$

Divide each term in $- 7 x = 18 - 2 y$ by $- 7$ and simplify.

Divide each term in $- 7 x = 18 - 2 y$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{18}{- 7} + \frac{- 2 y}{- 7}$

$6 x + 6 y = 0$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{18}{- 7} + \frac{- 2 y}{- 7}$

$6 x + 6 y = 0$

Divide $x$ by $1$ .

$x = \frac{18}{- 7} + \frac{- 2 y}{- 7}$

$6 x + 6 y = 0$

$x = \frac{18}{- 7} + \frac{- 2 y}{- 7}$

$6 x + 6 y = 0$

$x = \frac{18}{- 7} + \frac{- 2 y}{- 7}$

$6 x + 6 y = 0$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{18}{7} + \frac{- 2 y}{- 7}$

$6 x + 6 y = 0$

Dividing two negative values results in a positive value.

$x = - \frac{18}{7} + \frac{2 y}{7}$

$6 x + 6 y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$6 x + 6 y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$6 x + 6 y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$6 x + 6 y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$6 x + 6 y = 0$

Step 2

Replace all occurrences of $x$ with $- \frac{18}{7} + \frac{2 y}{7}$ in each equation.

Replace all occurrences of $x$ in $6 x + 6 y = 0$ with $- \frac{18}{7} + \frac{2 y}{7}$ .

$6 (- \frac{18}{7} + \frac{2 y}{7}) + 6 y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Simplify the left side.

Simplify $6 (- \frac{18}{7} + \frac{2 y}{7}) + 6 y$ .

Simplify each term.

Apply the distributive property.

$6 (- \frac{18}{7}) + 6 (\frac{2 y}{7}) + 6 y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Multiply $6 (- \frac{18}{7})$ .

Multiply $- 1$ by $6$ .

$- 6 (\frac{18}{7}) + 6 (\frac{2 y}{7}) + 6 y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Combine $- 6$ and $\frac{18}{7}$ .

$\frac{- 6 \cdot 18}{7} + 6 (\frac{2 y}{7}) + 6 y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Multiply $- 6$ by $18$ .

$\frac{- 108}{7} + 6 (\frac{2 y}{7}) + 6 y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$\frac{- 108}{7} + 6 (\frac{2 y}{7}) + 6 y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Multiply $6 \frac{2 y}{7}$ .

Combine $6$ and $\frac{2 y}{7}$ .

$\frac{- 108}{7} + \frac{6 (2 y)}{7} + 6 y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Multiply $2$ by $6$ .

$\frac{- 108}{7} + \frac{12 y}{7} + 6 y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$\frac{- 108}{7} + \frac{12 y}{7} + 6 y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Move the negative in front of the fraction.

$- \frac{108}{7} + \frac{12 y}{7} + 6 y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$- \frac{108}{7} + \frac{12 y}{7} + 6 y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

To write $6 y$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{108}{7} + \frac{12 y}{7} + 6 y \cdot \frac{7}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Combine $6 y$ and $\frac{7}{7}$ .

$- \frac{108}{7} + \frac{12 y}{7} + \frac{6 y \cdot 7}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Combine the numerators over the common denominator.

$- \frac{108}{7} + \frac{12 y + 6 y \cdot 7}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Combine the numerators over the common denominator.

$\frac{- 108 + 12 y + 6 y \cdot 7}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Multiply $7$ by $6$ .

$\frac{- 108 + 12 y + 42 y}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Add $12 y$ and $42 y$ .

$\frac{- 108 + 54 y}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Factor $54$ out of $- 108 + 54 y$ .

Factor $54$ out of $- 108$ .

$\frac{54 \cdot - 2 + 54 y}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Factor $54$ out of $54 \cdot - 2 + 54 y$ .

$\frac{54 (- 2 + y)}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$\frac{54 (- 2 + y)}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{54 (- 1 \cdot 2 + y)}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Factor $- 1$ out of $y$ .

$\frac{54 (- 1 \cdot 2 - 1 (- y))}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Factor $- 1$ out of $- 1 (2) - 1 (- y)$ .

$\frac{54 (- 1 (2 - y))}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Move the negative in front of the fraction.

$- \frac{54 (2 - y)}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$- \frac{54 (2 - y)}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$- \frac{54 (2 - y)}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$- \frac{54 (2 - y)}{7} = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Step 3

Solve for $y$ in $- \frac{54 (2 - y)}{7} = 0$ .

Set the numerator equal to zero.

$54 (2 - y) = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Solve the equation for $y$ .

Divide each term in $54 (2 - y) = 0$ by $54$ and simplify.

Divide each term in $54 (2 - y) = 0$ by $54$ .

$\frac{54 (2 - y)}{54} = \frac{0}{54}$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Simplify the left side.

Cancel the common factor of $54$ .

Cancel the common factor.

$\frac{54 (2 - y)}{54} = \frac{0}{54}$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Divide $2 - y$ by $1$ .

$2 - y = \frac{0}{54}$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$2 - y = \frac{0}{54}$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$2 - y = \frac{0}{54}$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Simplify the right side.

Divide $0$ by $54$ .

$2 - y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$2 - y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$2 - y = 0$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Subtract $2$ from both sides of the equation.

$- y = - 2$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Divide each term in $- y = - 2$ by $- 1$ and simplify.

Divide each term in $- y = - 2$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 2}{- 1}$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 2}{- 1}$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Divide $y$ by $1$ .

$y = \frac{- 2}{- 1}$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$y = \frac{- 2}{- 1}$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$y = 2$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$y = 2$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$y = 2$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$y = 2$

$x = - \frac{18}{7} + \frac{2 y}{7}$

$y = 2$

$x = - \frac{18}{7} + \frac{2 y}{7}$

Step 4

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

Replace all occurrences of $y$ in $x = - \frac{18}{7} + \frac{2 y}{7}$ with $2$ .

$x = - \frac{18}{7} + \frac{2 (2)}{7}$

$y = 2$

Simplify the right side.

Simplify $- \frac{18}{7} + \frac{2 (2)}{7}$ .

Combine the numerators over the common denominator.

$x = \frac{- 18 + 2 (2)}{7}$

$y = 2$

Simplify the expression.

Multiply $2$ by $2$ .

$x = \frac{- 18 + 4}{7}$

$y = 2$

Add $- 18$ and $4$ .

$x = \frac{- 14}{7}$

$y = 2$

Divide $- 14$ by $7$ .

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

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

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