Solve by Substitution 3x-4y=9 , -3x+2y=9

$3 x - 4 y = 9$ , $- 3 x + 2 y = 9$

Step 1

Solve for $x$ in $3 x - 4 y = 9$ .

Add $4 y$ to both sides of the equation.

$3 x = 9 + 4 y$

$- 3 x + 2 y = 9$

Divide each term in $3 x = 9 + 4 y$ by $3$ and simplify.

Divide each term in $3 x = 9 + 4 y$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3} + \frac{4 y}{3}$

$- 3 x + 2 y = 9$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3} + \frac{4 y}{3}$

$- 3 x + 2 y = 9$

Divide $x$ by $1$ .

$x = \frac{9}{3} + \frac{4 y}{3}$

$- 3 x + 2 y = 9$

$x = \frac{9}{3} + \frac{4 y}{3}$

$- 3 x + 2 y = 9$

$x = \frac{9}{3} + \frac{4 y}{3}$

$- 3 x + 2 y = 9$

Simplify the right side.

Divide $9$ by $3$ .

$x = 3 + \frac{4 y}{3}$

$- 3 x + 2 y = 9$

$x = 3 + \frac{4 y}{3}$

$- 3 x + 2 y = 9$

$x = 3 + \frac{4 y}{3}$

$- 3 x + 2 y = 9$

$x = 3 + \frac{4 y}{3}$

$- 3 x + 2 y = 9$

Step 2

Replace all occurrences of $x$ with $3 + \frac{4 y}{3}$ in each equation.

Replace all occurrences of $x$ in $- 3 x + 2 y = 9$ with $3 + \frac{4 y}{3}$ .

$- 3 (3 + \frac{4 y}{3}) + 2 y = 9$

$x = 3 + \frac{4 y}{3}$

Simplify the left side.

Simplify $- 3 (3 + \frac{4 y}{3}) + 2 y$ .

Simplify each term.

Apply the distributive property.

$- 3 \cdot 3 - 3 \frac{4 y}{3} + 2 y = 9$

$x = 3 + \frac{4 y}{3}$

Multiply $- 3$ by $3$ .

$- 9 - 3 \frac{4 y}{3} + 2 y = 9$

$x = 3 + \frac{4 y}{3}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$- 9 + 3 (- 1) (\frac{4 y}{3}) + 2 y = 9$

$x = 3 + \frac{4 y}{3}$

Cancel the common factor.

$- 9 + 3 \cdot (- 1 \frac{4 y}{3}) + 2 y = 9$

$x = 3 + \frac{4 y}{3}$

Rewrite the expression.

$- 9 - 1 (4 y) + 2 y = 9$

$x = 3 + \frac{4 y}{3}$

$- 9 - 1 (4 y) + 2 y = 9$

$x = 3 + \frac{4 y}{3}$

Multiply $4$ by $- 1$ .

$- 9 - 4 y + 2 y = 9$

$x = 3 + \frac{4 y}{3}$

$- 9 - 4 y + 2 y = 9$

$x = 3 + \frac{4 y}{3}$

Add $- 4 y$ and $2 y$ .

$- 9 - 2 y = 9$

$x = 3 + \frac{4 y}{3}$

$- 9 - 2 y = 9$

$x = 3 + \frac{4 y}{3}$

$- 9 - 2 y = 9$

$x = 3 + \frac{4 y}{3}$

$- 9 - 2 y = 9$

$x = 3 + \frac{4 y}{3}$

Step 3

Solve for $y$ in $- 9 - 2 y = 9$ .

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

Add $9$ to both sides of the equation.

$- 2 y = 9 + 9$

$x = 3 + \frac{4 y}{3}$

Add $9$ and $9$ .

$- 2 y = 18$

$x = 3 + \frac{4 y}{3}$

$- 2 y = 18$

$x = 3 + \frac{4 y}{3}$

Divide each term in $- 2 y = 18$ by $- 2$ and simplify.

Divide each term in $- 2 y = 18$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{18}{- 2}$

$x = 3 + \frac{4 y}{3}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{18}{- 2}$

$x = 3 + \frac{4 y}{3}$

Divide $y$ by $1$ .

$y = \frac{18}{- 2}$

$x = 3 + \frac{4 y}{3}$

$y = \frac{18}{- 2}$

$x = 3 + \frac{4 y}{3}$

$y = \frac{18}{- 2}$

$x = 3 + \frac{4 y}{3}$

Simplify the right side.

Divide $18$ by $- 2$ .

$y = - 9$

$x = 3 + \frac{4 y}{3}$

$y = - 9$

$x = 3 + \frac{4 y}{3}$

$y = - 9$

$x = 3 + \frac{4 y}{3}$

$y = - 9$

$x = 3 + \frac{4 y}{3}$

Step 4

Replace all occurrences of $y$ with $- 9$ in each equation.

Replace all occurrences of $y$ in $x = 3 + \frac{4 y}{3}$ with $- 9$ .

$x = 3 + \frac{4 (- 9)}{3}$

$y = - 9$

Simplify the right side.

Simplify $3 + \frac{4 (- 9)}{3}$ .

Multiply $4$ by $- 9$ .

$x = 3 + \frac{- 36}{3}$

$y = - 9$

Divide $- 36$ by $3$ .

$x = 3 - 12$

$y = - 9$

Subtract $12$ from $3$ .

$x = - 9$

$y = - 9$

$x = - 9$

$y = - 9$

$x = - 9$

$y = - 9$

$x = - 9$

$y = - 9$

Step 5

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

$(- 9, - 9)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 9, - 9)$

Equation Form:

$x = - 9, y = - 9$

Step 7

Solve by Substitution 3x-4y=9 , -3x+2y=9

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