Solve by Substitution -4x+9y=9 , x-3y=-6

$- 4 x + 9 y = 9$ , $x - 3 y = - 6$

Step 1

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

$x = - 6 + 3 y$

$- 4 x + 9 y = 9$

Step 2

Replace all occurrences of $x$ with $- 6 + 3 y$ in each equation.

Replace all occurrences of $x$ in $- 4 x + 9 y = 9$ with $- 6 + 3 y$ .

$- 4 (- 6 + 3 y) + 9 y = 9$

$x = - 6 + 3 y$

Simplify the left side.

Simplify $- 4 (- 6 + 3 y) + 9 y$ .

Simplify each term.

Apply the distributive property.

$- 4 \cdot - 6 - 4 (3 y) + 9 y = 9$

$x = - 6 + 3 y$

Multiply $- 4$ by $- 6$ .

$24 - 4 (3 y) + 9 y = 9$

$x = - 6 + 3 y$

Multiply $3$ by $- 4$ .

$24 - 12 y + 9 y = 9$

$x = - 6 + 3 y$

$24 - 12 y + 9 y = 9$

$x = - 6 + 3 y$

Add $- 12 y$ and $9 y$ .

$24 - 3 y = 9$

$x = - 6 + 3 y$

$24 - 3 y = 9$

$x = - 6 + 3 y$

$24 - 3 y = 9$

$x = - 6 + 3 y$

$24 - 3 y = 9$

$x = - 6 + 3 y$

Step 3

Solve for $y$ in $24 - 3 y = 9$ .

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

Subtract $24$ from both sides of the equation.

$- 3 y = 9 - 24$

$x = - 6 + 3 y$

Subtract $24$ from $9$ .

$- 3 y = - 15$

$x = - 6 + 3 y$

$- 3 y = - 15$

$x = - 6 + 3 y$

Divide each term in $- 3 y = - 15$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 15$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 15}{- 3}$

$x = - 6 + 3 y$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 15}{- 3}$

$x = - 6 + 3 y$

Divide $y$ by $1$ .

$y = \frac{- 15}{- 3}$

$x = - 6 + 3 y$

$y = \frac{- 15}{- 3}$

$x = - 6 + 3 y$

$y = \frac{- 15}{- 3}$

$x = - 6 + 3 y$

Simplify the right side.

Divide $- 15$ by $- 3$ .

$y = 5$

$x = - 6 + 3 y$

$y = 5$

$x = - 6 + 3 y$

$y = 5$

$x = - 6 + 3 y$

$y = 5$

$x = - 6 + 3 y$

Step 4

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

Replace all occurrences of $y$ in $x = - 6 + 3 y$ with $5$ .

$x = - 6 + 3 (5)$

$y = 5$

Simplify the right side.

Simplify $- 6 + 3 (5)$ .

Multiply $3$ by $5$ .

$x = - 6 + 15$

$y = 5$

Add $- 6$ and $15$ .

$x = 9$

$y = 5$

$x = 9$

$y = 5$

$x = 9$

$y = 5$

$x = 9$

$y = 5$

Step 5

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

$(9, 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(9, 5)$

Equation Form:

$x = 9, y = 5$

Step 7

Solve by Substitution -4x+9y=9 , x-3y=-6

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