Solve by Substitution 6x-y=-4 , 2x+2y=15

$6 x - y = - 4$ , $2 x + 2 y = 15$

Step 1

Solve for $x$ in $6 x - y = - 4$ .

Add $y$ to both sides of the equation.

$6 x = - 4 + y$

$2 x + 2 y = 15$

Divide each term in $6 x = - 4 + y$ by $6$ and simplify.

Divide each term in $6 x = - 4 + y$ by $6$ .

$\frac{6 x}{6} = \frac{- 4}{6} + \frac{y}{6}$

$2 x + 2 y = 15$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 4}{6} + \frac{y}{6}$

$2 x + 2 y = 15$

Divide $x$ by $1$ .

$x = \frac{- 4}{6} + \frac{y}{6}$

$2 x + 2 y = 15$

$x = \frac{- 4}{6} + \frac{y}{6}$

$2 x + 2 y = 15$

$x = \frac{- 4}{6} + \frac{y}{6}$

$2 x + 2 y = 15$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 4$ and $6$ .

Factor $2$ out of $- 4$ .

$x = \frac{2 (- 2)}{6} + \frac{y}{6}$

$2 x + 2 y = 15$

Cancel the common factors.

Factor $2$ out of $6$ .

$x = \frac{2 \cdot - 2}{2 \cdot 3} + \frac{y}{6}$

$2 x + 2 y = 15$

Cancel the common factor.

$x = \frac{2 \cdot - 2}{2 \cdot 3} + \frac{y}{6}$

$2 x + 2 y = 15$

Rewrite the expression.

$x = \frac{- 2}{3} + \frac{y}{6}$

$2 x + 2 y = 15$

$x = \frac{- 2}{3} + \frac{y}{6}$

$2 x + 2 y = 15$

$x = \frac{- 2}{3} + \frac{y}{6}$

$2 x + 2 y = 15$

Move the negative in front of the fraction.

$x = - \frac{2}{3} + \frac{y}{6}$

$2 x + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

$2 x + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

$2 x + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

$2 x + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

$2 x + 2 y = 15$

Step 2

Replace all occurrences of $x$ with $- \frac{2}{3} + \frac{y}{6}$ in each equation.

Replace all occurrences of $x$ in $2 x + 2 y = 15$ with $- \frac{2}{3} + \frac{y}{6}$ .

$2 (- \frac{2}{3} + \frac{y}{6}) + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Simplify the left side.

Simplify $2 (- \frac{2}{3} + \frac{y}{6}) + 2 y$ .

Simplify each term.

Apply the distributive property.

$2 (- \frac{2}{3}) + 2 (\frac{y}{6}) + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Multiply $2 (- \frac{2}{3})$ .

Multiply $- 1$ by $2$ .

$- 2 (\frac{2}{3}) + 2 (\frac{y}{6}) + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Combine $- 2$ and $\frac{2}{3}$ .

$\frac{- 2 \cdot 2}{3} + 2 (\frac{y}{6}) + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Multiply $- 2$ by $2$ .

$\frac{- 4}{3} + 2 (\frac{y}{6}) + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

$\frac{- 4}{3} + 2 (\frac{y}{6}) + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{- 4}{3} + 2 (\frac{y}{2 (3)}) + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Cancel the common factor.

$\frac{- 4}{3} + 2 (\frac{y}{2 \cdot 3}) + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Rewrite the expression.

$\frac{- 4}{3} + \frac{y}{3} + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

$\frac{- 4}{3} + \frac{y}{3} + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Move the negative in front of the fraction.

$- \frac{4}{3} + \frac{y}{3} + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

$- \frac{4}{3} + \frac{y}{3} + 2 y = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

To write $2 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{4}{3} + \frac{y}{3} + 2 y \cdot \frac{3}{3} = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Combine $2 y$ and $\frac{3}{3}$ .

$- \frac{4}{3} + \frac{y}{3} + \frac{2 y \cdot 3}{3} = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Combine the numerators over the common denominator.

$- \frac{4}{3} + \frac{y + 2 y \cdot 3}{3} = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Combine the numerators over the common denominator.

$\frac{- 4 + y + 2 y \cdot 3}{3} = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Multiply $3$ by $2$ .

$\frac{- 4 + y + 6 y}{3} = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Add $y$ and $6 y$ .

$\frac{- 4 + 7 y}{3} = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- 1 \cdot 4 + 7 y}{3} = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Factor $- 1$ out of $7 y$ .

$\frac{- 1 \cdot 4 - (- 7 y)}{3} = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Factor $- 1$ out of $- 1 (4) - (- 7 y)$ .

$\frac{- 1 (4 - 7 y)}{3} = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Move the negative in front of the fraction.

$- \frac{4 - 7 y}{3} = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

$- \frac{4 - 7 y}{3} = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

$- \frac{4 - 7 y}{3} = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

$- \frac{4 - 7 y}{3} = 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Step 3

Solve for $y$ in $- \frac{4 - 7 y}{3} = 15$ .

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{4 - 7 y}{3}) = - 3 \cdot 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{4 - 7 y}{3}$ into the numerator.

$- 3 \frac{- (4 - 7 y)}{3} = - 3 \cdot 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Factor $3$ out of $- 3$ .

$3 (- 1) (\frac{- (4 - 7 y)}{3}) = - 3 \cdot 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Cancel the common factor.

$3 \cdot (- 1 \frac{- (4 - 7 y)}{3}) = - 3 \cdot 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Rewrite the expression.

$4 - 7 y = - 3 \cdot 15$

$x = - \frac{2}{3} + \frac{y}{6}$

$4 - 7 y = - 3 \cdot 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (4 - 7 y) = - 3 \cdot 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Multiply $4 - 7 y$ by $1$ .

$4 - 7 y = - 3 \cdot 15$

$x = - \frac{2}{3} + \frac{y}{6}$

$4 - 7 y = - 3 \cdot 15$

$x = - \frac{2}{3} + \frac{y}{6}$

$4 - 7 y = - 3 \cdot 15$

$x = - \frac{2}{3} + \frac{y}{6}$

$4 - 7 y = - 3 \cdot 15$

$x = - \frac{2}{3} + \frac{y}{6}$

Simplify the right side.

Multiply $- 3$ by $15$ .

$4 - 7 y = - 45$

$x = - \frac{2}{3} + \frac{y}{6}$

$4 - 7 y = - 45$

$x = - \frac{2}{3} + \frac{y}{6}$

$4 - 7 y = - 45$

$x = - \frac{2}{3} + \frac{y}{6}$

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

Subtract $4$ from both sides of the equation.

$- 7 y = - 45 - 4$

$x = - \frac{2}{3} + \frac{y}{6}$

Subtract $4$ from $- 45$ .

$- 7 y = - 49$

$x = - \frac{2}{3} + \frac{y}{6}$

$- 7 y = - 49$

$x = - \frac{2}{3} + \frac{y}{6}$

Divide each term in $- 7 y = - 49$ by $- 7$ and simplify.

Divide each term in $- 7 y = - 49$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 49}{- 7}$

$x = - \frac{2}{3} + \frac{y}{6}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 49}{- 7}$

$x = - \frac{2}{3} + \frac{y}{6}$

Divide $y$ by $1$ .

$y = \frac{- 49}{- 7}$

$x = - \frac{2}{3} + \frac{y}{6}$

$y = \frac{- 49}{- 7}$

$x = - \frac{2}{3} + \frac{y}{6}$

$y = \frac{- 49}{- 7}$

$x = - \frac{2}{3} + \frac{y}{6}$

Simplify the right side.

Divide $- 49$ by $- 7$ .

$y = 7$

$x = - \frac{2}{3} + \frac{y}{6}$

$y = 7$

$x = - \frac{2}{3} + \frac{y}{6}$

$y = 7$

$x = - \frac{2}{3} + \frac{y}{6}$

$y = 7$

$x = - \frac{2}{3} + \frac{y}{6}$

Step 4

Replace all occurrences of $y$ with $7$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{2}{3} + \frac{y}{6}$ with $7$ .

$x = - \frac{2}{3} + \frac{7}{6}$

$y = 7$

Simplify the right side.

Simplify $- \frac{2}{3} + \frac{7}{6}$ .

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = - \frac{2}{3} \cdot \frac{2}{2} + \frac{7}{6}$

$y = 7$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

$x = - \frac{2 \cdot 2}{3 \cdot 2} + \frac{7}{6}$

$y = 7$

Multiply $3$ by $2$ .

$x = - \frac{2 \cdot 2}{6} + \frac{7}{6}$

$y = 7$

$x = - \frac{2 \cdot 2}{6} + \frac{7}{6}$

$y = 7$

Combine the numerators over the common denominator.

$x = \frac{- 2 \cdot 2 + 7}{6}$

$y = 7$

Simplify the numerator.

Multiply $- 2$ by $2$ .

$x = \frac{- 4 + 7}{6}$

$y = 7$

Add $- 4$ and $7$ .

$x = \frac{3}{6}$

$y = 7$

$x = \frac{3}{6}$

$y = 7$

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$x = \frac{3 (1)}{6}$

$y = 7$

Cancel the common factors.

Factor $3$ out of $6$ .

$x = \frac{3 \cdot 1}{3 \cdot 2}$

$y = 7$

Cancel the common factor.

$x = \frac{3 \cdot 1}{3 \cdot 2}$

$y = 7$

Rewrite the expression.

$x = \frac{1}{2}$

$y = 7$

$x = \frac{1}{2}$

$y = 7$

$x = \frac{1}{2}$

$y = 7$

$x = \frac{1}{2}$

$y = 7$

$x = \frac{1}{2}$

$y = 7$

$x = \frac{1}{2}$

$y = 7$

Step 5

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

$(\frac{1}{2}, 7)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{1}{2}, 7)$

Equation Form:

$x = \frac{1}{2}, y = 7$

Step 7

Solve by Substitution 6x-y=-4 , 2x+2y=15

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