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

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

Step 1

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

Add $y$ to both sides of the equation.

$3 x = 4 + y$

$2 x - 3 y = - 9$

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

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

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

$2 x - 3 y = - 9$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

$2 x - 3 y = - 9$

Divide $x$ by $1$ .

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

$2 x - 3 y = - 9$

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

$2 x - 3 y = - 9$

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

$2 x - 3 y = - 9$

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

$2 x - 3 y = - 9$

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

$2 x - 3 y = - 9$

Step 2

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

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

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

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

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

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

Multiply $2 (\frac{4}{3})$ .

Combine $2$ and $\frac{4}{3}$ .

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

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

Multiply $2$ by $4$ .

$\frac{8}{3} + 2 (\frac{y}{3}) - 3 y = - 9$

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

$\frac{8}{3} + 2 (\frac{y}{3}) - 3 y = - 9$

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

Combine $2$ and $\frac{y}{3}$ .

$\frac{8}{3} + \frac{2 y}{3} - 3 y = - 9$

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

$\frac{8}{3} + \frac{2 y}{3} - 3 y = - 9$

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

To write $- 3 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{8}{3} + \frac{2 y}{3} - 3 y \cdot \frac{3}{3} = - 9$

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

Combine $- 3 y$ and $\frac{3}{3}$ .

$\frac{8}{3} + \frac{2 y}{3} + \frac{- 3 y \cdot 3}{3} = - 9$

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

Combine the numerators over the common denominator.

$\frac{8}{3} + \frac{2 y - 3 y \cdot 3}{3} = - 9$

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

Combine the numerators over the common denominator.

$\frac{8 + 2 y - 3 y \cdot 3}{3} = - 9$

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

Multiply $3$ by $- 3$ .

$\frac{8 + 2 y - 9 y}{3} = - 9$

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

Subtract $9 y$ from $2 y$ .

$\frac{8 - 7 y}{3} = - 9$

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

$\frac{8 - 7 y}{3} = - 9$

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

$\frac{8 - 7 y}{3} = - 9$

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

$\frac{8 - 7 y}{3} = - 9$

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

Step 3

Solve for $y$ in $\frac{8 - 7 y}{3} = - 9$ .

Multiply both sides by $3$ .

$\frac{8 - 7 y}{3} \cdot 3 = - 9 \cdot 3$

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

Simplify.

Simplify the left side.

Simplify $\frac{8 - 7 y}{3} \cdot 3$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{8 - 7 y}{3} \cdot 3 = - 9 \cdot 3$

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

Rewrite the expression.

$8 - 7 y = - 9 \cdot 3$

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

$8 - 7 y = - 9 \cdot 3$

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

Reorder $8$ and $- 7 y$ .

$- 7 y + 8 = - 9 \cdot 3$

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

$- 7 y + 8 = - 9 \cdot 3$

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

$- 7 y + 8 = - 9 \cdot 3$

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

Simplify the right side.

Multiply $- 9$ by $3$ .

$- 7 y + 8 = - 27$

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

$- 7 y + 8 = - 27$

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

$- 7 y + 8 = - 27$

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

Solve for $y$ .

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

Subtract $8$ from both sides of the equation.

$- 7 y = - 27 - 8$

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

Subtract $8$ from $- 27$ .

$- 7 y = - 35$

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

$- 7 y = - 35$

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

Divide each term in $- 7 y = - 35$ by $- 7$ and simplify.

Divide each term in $- 7 y = - 35$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 35}{- 7}$

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

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 35}{- 7}$

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

Divide $y$ by $1$ .

$y = \frac{- 35}{- 7}$

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

$y = \frac{- 35}{- 7}$

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

$y = \frac{- 35}{- 7}$

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

Simplify the right side.

Divide $- 35$ by $- 7$ .

$y = 5$

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

$y = 5$

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

$y = 5$

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

$y = 5$

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

$y = 5$

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

Step 4

Replace all occurrences of $y$ with $5$ in each equation.

Replace all occurrences of $y$ in $x = \frac{4}{3} + \frac{y}{3}$ with $5$ .

$x = \frac{4}{3} + \frac{5}{3}$

$y = 5$

Simplify the right side.

Simplify $\frac{4}{3} + \frac{5}{3}$ .

Combine the numerators over the common denominator.

$x = \frac{4 + 5}{3}$

$y = 5$

Simplify the expression.

Add $4$ and $5$ .

$x = \frac{9}{3}$

$y = 5$

Divide $9$ by $3$ .

$x = 3$

$y = 5$

$x = 3$

$y = 5$

$x = 3$

$y = 5$

$x = 3$

$y = 5$

$x = 3$

$y = 5$

Step 5

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

$(3, 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, 5)$

Equation Form:

$x = 3, y = 5$

Step 7

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

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