Solve by Substitution -5x+2y=-42 6x=y

$- 5 x + 2 y = - 42$ $6 x = y$

Step 1

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

Divide each term in $6 x = y$ by $6$ .

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

$- 5 x + 2 y = - 42$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

$- 5 x + 2 y = - 42$

Divide $x$ by $1$ .

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

$- 5 x + 2 y = - 42$

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

$- 5 x + 2 y = - 42$

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

$- 5 x + 2 y = - 42$

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

$- 5 x + 2 y = - 42$

Step 2

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

Replace all occurrences of $x$ in $- 5 x + 2 y = - 42$ with $\frac{y}{6}$ .

$- 5 \frac{y}{6} + 2 y = - 42$

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

Simplify the left side.

Simplify $- 5 \frac{y}{6} + 2 y$ .

Simplify each term.

Combine $- 5$ and $\frac{y}{6}$ .

$\frac{- 5 y}{6} + 2 y = - 42$

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

Move the negative in front of the fraction.

$- \frac{5 y}{6} + 2 y = - 42$

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

$- \frac{5 y}{6} + 2 y = - 42$

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

To write $2 y$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- \frac{5 y}{6} + 2 y \cdot \frac{6}{6} = - 42$

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

Simplify terms.

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

$- \frac{5 y}{6} + \frac{2 y \cdot 6}{6} = - 42$

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

Combine the numerators over the common denominator.

$\frac{- 5 y + 2 y \cdot 6}{6} = - 42$

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

$\frac{- 5 y + 2 y \cdot 6}{6} = - 42$

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

Simplify the numerator.

Factor $y$ out of $- 5 y + 2 y \cdot 6$ .

Factor $y$ out of $- 5 y$ .

$\frac{y \cdot - 5 + 2 y \cdot 6}{6} = - 42$

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

Factor $y$ out of $2 y \cdot 6$ .

$\frac{y \cdot - 5 + y (2 \cdot 6)}{6} = - 42$

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

Factor $y$ out of $y \cdot - 5 + y (2 \cdot 6)$ .

$\frac{y (- 5 + 2 \cdot 6)}{6} = - 42$

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

$\frac{y (- 5 + 2 \cdot 6)}{6} = - 42$

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

Multiply $2$ by $6$ .

$\frac{y (- 5 + 12)}{6} = - 42$

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

Add $- 5$ and $12$ .

$\frac{y \cdot 7}{6} = - 42$

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

$\frac{y \cdot 7}{6} = - 42$

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

Move $7$ to the left of $y$ .

$\frac{7 y}{6} = - 42$

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

$\frac{7 y}{6} = - 42$

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

$\frac{7 y}{6} = - 42$

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

$\frac{7 y}{6} = - 42$

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

Step 3

Solve for $y$ in $\frac{7 y}{6} = - 42$ .

Multiply both sides of the equation by $\frac{6}{7}$ .

$\frac{6}{7} \cdot \frac{7 y}{6} = \frac{6}{7} \cdot - 42$

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{6}{7} \cdot \frac{7 y}{6}$ .

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6}{7} \cdot \frac{7 y}{6} = \frac{6}{7} \cdot - 42$

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

Rewrite the expression.

$\frac{1}{7} \cdot (7 y) = \frac{6}{7} \cdot - 42$

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

$\frac{1}{7} \cdot (7 y) = \frac{6}{7} \cdot - 42$

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

Cancel the common factor of $7$ .

Factor $7$ out of $7 y$ .

$\frac{1}{7} \cdot (7 (y)) = \frac{6}{7} \cdot - 42$

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

Cancel the common factor.

$\frac{1}{7} \cdot (7 y) = \frac{6}{7} \cdot - 42$

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

Rewrite the expression.

$y = \frac{6}{7} \cdot - 42$

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

$y = \frac{6}{7} \cdot - 42$

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

$y = \frac{6}{7} \cdot - 42$

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

$y = \frac{6}{7} \cdot - 42$

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

Simplify the right side.

Simplify $\frac{6}{7} \cdot - 42$ .

Cancel the common factor of $7$ .

Factor $7$ out of $- 42$ .

$y = \frac{6}{7} \cdot (7 (- 6))$

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

Cancel the common factor.

$y = \frac{6}{7} \cdot (7 \cdot - 6)$

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

Rewrite the expression.

$y = 6 \cdot - 6$

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

$y = 6 \cdot - 6$

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

Multiply $6$ by $- 6$ .

$y = - 36$

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

$y = - 36$

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

$y = - 36$

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

$y = - 36$

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

$y = - 36$

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

Step 4

Replace all occurrences of $y$ with $- 36$ in each equation.

Replace all occurrences of $y$ in $x = \frac{y}{6}$ with $- 36$ .

$x = \frac{- 36}{6}$

$y = - 36$

Simplify the right side.

Divide $- 36$ by $6$ .

$x = - 6$

$y = - 36$

$x = - 6$

$y = - 36$

$x = - 6$

$y = - 36$

Step 5

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

$(- 6, - 36)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 6, - 36)$

Equation Form:

$x = - 6, y = - 36$

Step 7

Solve by Substitution -5x+2y=-42 6x=y

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