Solve the System of Equations -2x-3y=-10 and 6x+9y=30

$- 2 x - 3 y = - 10$ and $6 x + 9 y = 30$

Step 1

Solve for $x$ in $- 2 x - 3 y = - 10$ .

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

$- 2 x = - 10 + 3 y$

$6 x + 9 y = 30$

Divide each term in $- 2 x = - 10 + 3 y$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 10 + 3 y$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 10}{- 2} + \frac{3 y}{- 2}$

$6 x + 9 y = 30$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 10}{- 2} + \frac{3 y}{- 2}$

$6 x + 9 y = 30$

Divide $x$ by $1$ .

$x = \frac{- 10}{- 2} + \frac{3 y}{- 2}$

$6 x + 9 y = 30$

$x = \frac{- 10}{- 2} + \frac{3 y}{- 2}$

$6 x + 9 y = 30$

$x = \frac{- 10}{- 2} + \frac{3 y}{- 2}$

$6 x + 9 y = 30$

Simplify the right side.

Simplify each term.

Divide $- 10$ by $- 2$ .

$x = 5 + \frac{3 y}{- 2}$

$6 x + 9 y = 30$

Move the negative in front of the fraction.

$x = 5 - \frac{3 y}{2}$

$6 x + 9 y = 30$

$x = 5 - \frac{3 y}{2}$

$6 x + 9 y = 30$

$x = 5 - \frac{3 y}{2}$

$6 x + 9 y = 30$

$x = 5 - \frac{3 y}{2}$

$6 x + 9 y = 30$

$x = 5 - \frac{3 y}{2}$

$6 x + 9 y = 30$

Step 2

Replace all occurrences of $x$ with $5 - \frac{3 y}{2}$ in each equation.

Replace all occurrences of $x$ in $6 x + 9 y = 30$ with $5 - \frac{3 y}{2}$ .

$6 (5 - \frac{3 y}{2}) + 9 y = 30$

$x = 5 - \frac{3 y}{2}$

Simplify the left side.

Simplify $6 (5 - \frac{3 y}{2}) + 9 y$ .

Simplify each term.

Apply the distributive property.

$6 \cdot 5 + 6 (- \frac{3 y}{2}) + 9 y = 30$

$x = 5 - \frac{3 y}{2}$

Multiply $6$ by $5$ .

$30 + 6 (- \frac{3 y}{2}) + 9 y = 30$

$x = 5 - \frac{3 y}{2}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3 y}{2}$ into the numerator.

$30 + 6 (\frac{- 3 y}{2}) + 9 y = 30$

$x = 5 - \frac{3 y}{2}$

Factor $2$ out of $6$ .

$30 + 2 (3) (\frac{- 3 y}{2}) + 9 y = 30$

$x = 5 - \frac{3 y}{2}$

Cancel the common factor.

$30 + 2 \cdot (3 (\frac{- 3 y}{2})) + 9 y = 30$

$x = 5 - \frac{3 y}{2}$

Rewrite the expression.

$30 + 3 (- 3 y) + 9 y = 30$

$x = 5 - \frac{3 y}{2}$

$30 + 3 (- 3 y) + 9 y = 30$

$x = 5 - \frac{3 y}{2}$

Multiply $- 3$ by $3$ .

$30 - 9 y + 9 y = 30$

$x = 5 - \frac{3 y}{2}$

$30 - 9 y + 9 y = 30$

$x = 5 - \frac{3 y}{2}$

Combine the opposite terms in $30 - 9 y + 9 y$ .

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

$30 + 0 = 30$

$x = 5 - \frac{3 y}{2}$

Add $30$ and $0$ .

$30 = 30$

$x = 5 - \frac{3 y}{2}$

$30 = 30$

$x = 5 - \frac{3 y}{2}$

$30 = 30$

$x = 5 - \frac{3 y}{2}$

$30 = 30$

$x = 5 - \frac{3 y}{2}$

$30 = 30$

$x = 5 - \frac{3 y}{2}$

Step 3

Remove any equations from the system that are always true.

$x = 5 - \frac{3 y}{2}$

Step 4

Solve the System of Equations -2x-3y=-10 and 6x+9y=30

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