Solve by Substitution 2x-3y=-13 , y=2x+7

$2 x - 3 y = - 13$ , $y = 2 x + 7$

Step 1

Replace all occurrences of $y$ with $2 x + 7$ in each equation.

Replace all occurrences of $y$ in $2 x - 3 y = - 13$ with $2 x + 7$ .

$2 x - 3 (2 x + 7) = - 13$

$y = 2 x + 7$

Simplify the left side.

Simplify $2 x - 3 (2 x + 7)$ .

Simplify each term.

Apply the distributive property.

$2 x - 3 (2 x) - 3 \cdot 7 = - 13$

$y = 2 x + 7$

Multiply $2$ by $- 3$ .

$2 x - 6 x - 3 \cdot 7 = - 13$

$y = 2 x + 7$

Multiply $- 3$ by $7$ .

$2 x - 6 x - 21 = - 13$

$y = 2 x + 7$

$2 x - 6 x - 21 = - 13$

$y = 2 x + 7$

Subtract $6 x$ from $2 x$ .

$- 4 x - 21 = - 13$

$y = 2 x + 7$

$- 4 x - 21 = - 13$

$y = 2 x + 7$

$- 4 x - 21 = - 13$

$y = 2 x + 7$

$- 4 x - 21 = - 13$

$y = 2 x + 7$

Step 2

Solve for $x$ in $- 4 x - 21 = - 13$ .

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

Add $21$ to both sides of the equation.

$- 4 x = - 13 + 21$

$y = 2 x + 7$

Add $- 13$ and $21$ .

$- 4 x = 8$

$y = 2 x + 7$

$- 4 x = 8$

$y = 2 x + 7$

Divide each term in $- 4 x = 8$ by $- 4$ and simplify.

Divide each term in $- 4 x = 8$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{8}{- 4}$

$y = 2 x + 7$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{8}{- 4}$

$y = 2 x + 7$

Divide $x$ by $1$ .

$x = \frac{8}{- 4}$

$y = 2 x + 7$

$x = \frac{8}{- 4}$

$y = 2 x + 7$

$x = \frac{8}{- 4}$

$y = 2 x + 7$

Simplify the right side.

Divide $8$ by $- 4$ .

$x = - 2$

$y = 2 x + 7$

$x = - 2$

$y = 2 x + 7$

$x = - 2$

$y = 2 x + 7$

$x = - 2$

$y = 2 x + 7$

Step 3

Replace all occurrences of $x$ with $- 2$ in each equation.

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

$y = 2 (- 2) + 7$

$x = - 2$

Simplify the right side.

Simplify $2 (- 2) + 7$ .

Multiply $2$ by $- 2$ .

$y = - 4 + 7$

$x = - 2$

Add $- 4$ and $7$ .

$y = 3$

$x = - 2$

$y = 3$

$x = - 2$

$y = 3$

$x = - 2$

$y = 3$

$x = - 2$

Step 4

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

$(- 2, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 2, 3)$

Equation Form:

$x = - 2, y = 3$

Step 6

Solve by Substitution 2x-3y=-13 , y=2x+7

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