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

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

Step 1

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

$y = 7 + 3 x$

$2 x - 3 y = 7$

Step 2

Replace all occurrences of $y$ with $7 + 3 x$ in each equation.

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

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

$y = 7 + 3 x$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$y = 7 + 3 x$

Multiply $- 3$ by $7$ .

$2 x - 21 - 3 (3 x) = 7$

$y = 7 + 3 x$

Multiply $3$ by $- 3$ .

$2 x - 21 - 9 x = 7$

$y = 7 + 3 x$

$2 x - 21 - 9 x = 7$

$y = 7 + 3 x$

Subtract $9 x$ from $2 x$ .

$- 7 x - 21 = 7$

$y = 7 + 3 x$

$- 7 x - 21 = 7$

$y = 7 + 3 x$

$- 7 x - 21 = 7$

$y = 7 + 3 x$

$- 7 x - 21 = 7$

$y = 7 + 3 x$

Step 3

Solve for $x$ in $- 7 x - 21 = 7$ .

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

Add $21$ to both sides of the equation.

$- 7 x = 7 + 21$

$y = 7 + 3 x$

Add $7$ and $21$ .

$- 7 x = 28$

$y = 7 + 3 x$

$- 7 x = 28$

$y = 7 + 3 x$

Divide each term in $- 7 x = 28$ by $- 7$ and simplify.

Divide each term in $- 7 x = 28$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{28}{- 7}$

$y = 7 + 3 x$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{28}{- 7}$

$y = 7 + 3 x$

Divide $x$ by $1$ .

$x = \frac{28}{- 7}$

$y = 7 + 3 x$

$x = \frac{28}{- 7}$

$y = 7 + 3 x$

$x = \frac{28}{- 7}$

$y = 7 + 3 x$

Simplify the right side.

Divide $28$ by $- 7$ .

$x = - 4$

$y = 7 + 3 x$

$x = - 4$

$y = 7 + 3 x$

$x = - 4$

$y = 7 + 3 x$

$x = - 4$

$y = 7 + 3 x$

Step 4

Replace all occurrences of $x$ with $- 4$ in each equation.

Replace all occurrences of $x$ in $y = 7 + 3 x$ with $- 4$ .

$y = 7 + 3 (- 4)$

$x = - 4$

Simplify the right side.

Simplify $7 + 3 (- 4)$ .

Multiply $3$ by $- 4$ .

$y = 7 - 12$

$x = - 4$

Subtract $12$ from $7$ .

$y = - 5$

$x = - 4$

$y = - 5$

$x = - 4$

$y = - 5$

$x = - 4$

$y = - 5$

$x = - 4$

Step 5

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

$(- 4, - 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 4, - 5)$

Equation Form:

$x = - 4, y = - 5$

Step 7

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

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