Solve by Substitution x-3y=-6 , 2x-7y=10

$x - 3 y = - 6$ , $2 x - 7 y = 10$

Step 1

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

$x = - 6 + 3 y$

$2 x - 7 y = 10$

Step 2

Replace all occurrences of $x$ with $- 6 + 3 y$ in each equation.

Replace all occurrences of $x$ in $2 x - 7 y = 10$ with $- 6 + 3 y$ .

$2 (- 6 + 3 y) - 7 y = 10$

$x = - 6 + 3 y$

Simplify the left side.

Simplify $2 (- 6 + 3 y) - 7 y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot - 6 + 2 (3 y) - 7 y = 10$

$x = - 6 + 3 y$

Multiply $2$ by $- 6$ .

$- 12 + 2 (3 y) - 7 y = 10$

$x = - 6 + 3 y$

Multiply $3$ by $2$ .

$- 12 + 6 y - 7 y = 10$

$x = - 6 + 3 y$

$- 12 + 6 y - 7 y = 10$

$x = - 6 + 3 y$

Subtract $7 y$ from $6 y$ .

$- 12 - y = 10$

$x = - 6 + 3 y$

$- 12 - y = 10$

$x = - 6 + 3 y$

$- 12 - y = 10$

$x = - 6 + 3 y$

$- 12 - y = 10$

$x = - 6 + 3 y$

Step 3

Solve for $y$ in $- 12 - y = 10$ .

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

Add $12$ to both sides of the equation.

$- y = 10 + 12$

$x = - 6 + 3 y$

Add $10$ and $12$ .

$- y = 22$

$x = - 6 + 3 y$

$- y = 22$

$x = - 6 + 3 y$

Divide each term in $- y = 22$ by $- 1$ and simplify.

Divide each term in $- y = 22$ by $- 1$ .

$\frac{- y}{- 1} = \frac{22}{- 1}$

$x = - 6 + 3 y$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{22}{- 1}$

$x = - 6 + 3 y$

Divide $y$ by $1$ .

$y = \frac{22}{- 1}$

$x = - 6 + 3 y$

$y = \frac{22}{- 1}$

$x = - 6 + 3 y$

Simplify the right side.

Divide $22$ by $- 1$ .

$y = - 22$

$x = - 6 + 3 y$

$y = - 22$

$x = - 6 + 3 y$

$y = - 22$

$x = - 6 + 3 y$

$y = - 22$

$x = - 6 + 3 y$

Step 4

Replace all occurrences of $y$ with $- 22$ in each equation.

Replace all occurrences of $y$ in $x = - 6 + 3 y$ with $- 22$ .

$x = - 6 + 3 (- 22)$

$y = - 22$

Simplify the right side.

Simplify $- 6 + 3 (- 22)$ .

Multiply $3$ by $- 22$ .

$x = - 6 - 66$

$y = - 22$

Subtract $66$ from $- 6$ .

$x = - 72$

$y = - 22$

$x = - 72$

$y = - 22$

$x = - 72$

$y = - 22$

$x = - 72$

$y = - 22$

Step 5

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

$(- 72, - 22)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 72, - 22)$

Equation Form:

$x = - 72, y = - 22$

Step 7

Solve by Substitution x-3y=-6 , 2x-7y=10

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