Solve by Substitution x+3y=2 , 2x-3y=22

$x + 3 y = 2$ , $2 x - 3 y = 22$

Step 1

Subtract $3 y$ from both sides of the equation.

$x = 2 - 3 y$

$2 x - 3 y = 22$

Step 2

Replace all occurrences of $x$ with $2 - 3 y$ in each equation.

Replace all occurrences of $x$ in $2 x - 3 y = 22$ with $2 - 3 y$ .

$2 (2 - 3 y) - 3 y = 22$

$x = 2 - 3 y$

Simplify the left side.

Simplify $2 (2 - 3 y) - 3 y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot 2 + 2 (- 3 y) - 3 y = 22$

$x = 2 - 3 y$

Multiply $2$ by $2$ .

$4 + 2 (- 3 y) - 3 y = 22$

$x = 2 - 3 y$

Multiply $- 3$ by $2$ .

$4 - 6 y - 3 y = 22$

$x = 2 - 3 y$

$4 - 6 y - 3 y = 22$

$x = 2 - 3 y$

Subtract $3 y$ from $- 6 y$ .

$4 - 9 y = 22$

$x = 2 - 3 y$

$4 - 9 y = 22$

$x = 2 - 3 y$

$4 - 9 y = 22$

$x = 2 - 3 y$

$4 - 9 y = 22$

$x = 2 - 3 y$

Step 3

Solve for $y$ in $4 - 9 y = 22$ .

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

Subtract $4$ from both sides of the equation.

$- 9 y = 22 - 4$

$x = 2 - 3 y$

Subtract $4$ from $22$ .

$- 9 y = 18$

$x = 2 - 3 y$

$- 9 y = 18$

$x = 2 - 3 y$

Divide each term in $- 9 y = 18$ by $- 9$ and simplify.

Divide each term in $- 9 y = 18$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{18}{- 9}$

$x = 2 - 3 y$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{18}{- 9}$

$x = 2 - 3 y$

Divide $y$ by $1$ .

$y = \frac{18}{- 9}$

$x = 2 - 3 y$

$y = \frac{18}{- 9}$

$x = 2 - 3 y$

$y = \frac{18}{- 9}$

$x = 2 - 3 y$

Simplify the right side.

Divide $18$ by $- 9$ .

$y = - 2$

$x = 2 - 3 y$

$y = - 2$

$x = 2 - 3 y$

$y = - 2$

$x = 2 - 3 y$

$y = - 2$

$x = 2 - 3 y$

Step 4

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

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

$x = 2 - 3 \cdot - 2$

$y = - 2$

Simplify the right side.

Simplify $2 - 3 \cdot - 2$ .

Multiply $- 3$ by $- 2$ .

$x = 2 + 6$

$y = - 2$

Add $2$ and $6$ .

$x = 8$

$y = - 2$

$x = 8$

$y = - 2$

$x = 8$

$y = - 2$

$x = 8$

$y = - 2$

Step 5

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

$(8, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(8, - 2)$

Equation Form:

$x = 8, y = - 2$

Step 7

Solve by Substitution x+3y=2 , 2x-3y=22

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