Solve the System of Equations -2x+9y=-17 -x-3y=-1

$- 2 x + 9 y = - 17$ $- x - 3 y = - 1$

Step 1

Solve for $x$ in $- 2 x + 9 y = - 17$ .

Subtract $9 y$ from both sides of the equation.

$- 2 x = - 17 - 9 y$

$- x - 3 y = - 1$

Divide each term in $- 2 x = - 17 - 9 y$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 17 - 9 y$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 17}{- 2} + \frac{- 9 y}{- 2}$

$- x - 3 y = - 1$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 17}{- 2} + \frac{- 9 y}{- 2}$

$- x - 3 y = - 1$

Divide $x$ by $1$ .

$x = \frac{- 17}{- 2} + \frac{- 9 y}{- 2}$

$- x - 3 y = - 1$

$x = \frac{- 17}{- 2} + \frac{- 9 y}{- 2}$

$- x - 3 y = - 1$

$x = \frac{- 17}{- 2} + \frac{- 9 y}{- 2}$

$- x - 3 y = - 1$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$x = \frac{17}{2} + \frac{- 9 y}{- 2}$

$- x - 3 y = - 1$

Dividing two negative values results in a positive value.

$x = \frac{17}{2} + \frac{9 y}{2}$

$- x - 3 y = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

$- x - 3 y = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

$- x - 3 y = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

$- x - 3 y = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

$- x - 3 y = - 1$

Step 2

Replace all occurrences of $x$ with $\frac{17}{2} + \frac{9 y}{2}$ in each equation.

Replace all occurrences of $x$ in $- x - 3 y = - 1$ with $\frac{17}{2} + \frac{9 y}{2}$ .

$- (\frac{17}{2} + \frac{9 y}{2}) - 3 y = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Simplify the left side.

Simplify $- (\frac{17}{2} + \frac{9 y}{2}) - 3 y$ .

Apply the distributive property.

$- \frac{17}{2} - \frac{9 y}{2} - 3 y = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

To write $- 3 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{17}{2} - \frac{9 y}{2} - 3 y \cdot \frac{2}{2} = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

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

$- \frac{17}{2} - \frac{9 y}{2} + \frac{- 3 y \cdot 2}{2} = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Combine the numerators over the common denominator.

$- \frac{17}{2} + \frac{- 9 y - 3 y \cdot 2}{2} = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Combine the numerators over the common denominator.

$\frac{- 17 - 9 y - 3 y \cdot 2}{2} = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Multiply $2$ by $- 3$ .

$\frac{- 17 - 9 y - 6 y}{2} = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Subtract $6 y$ from $- 9 y$ .

$\frac{- 17 - 15 y}{2} = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Rewrite $- 17$ as $- 1 (17)$ .

$\frac{- 1 \cdot 17 - 15 y}{2} = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Factor $- 1$ out of $- 15 y$ .

$\frac{- 1 \cdot 17 - (15 y)}{2} = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Factor $- 1$ out of $- 1 (17) - (15 y)$ .

$\frac{- 1 (17 + 15 y)}{2} = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Move the negative in front of the fraction.

$- \frac{17 + 15 y}{2} = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

$- \frac{17 + 15 y}{2} = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

$- \frac{17 + 15 y}{2} = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

$- \frac{17 + 15 y}{2} = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Step 3

Solve for $y$ in $- \frac{17 + 15 y}{2} = - 1$ .

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{17 + 15 y}{2}) = - 2 \cdot - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{17 + 15 y}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{17 + 15 y}{2}$ into the numerator.

$- 2 \frac{- (17 + 15 y)}{2} = - 2 \cdot - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Factor $2$ out of $- 2$ .

$2 (- 1) (\frac{- (17 + 15 y)}{2}) = - 2 \cdot - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Cancel the common factor.

$2 \cdot (- 1 \frac{- (17 + 15 y)}{2}) = - 2 \cdot - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Rewrite the expression.

$17 + 15 y = - 2 \cdot - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

$17 + 15 y = - 2 \cdot - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (17 + 15 y) = - 2 \cdot - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Multiply $17 + 15 y$ by $1$ .

$17 + 15 y = - 2 \cdot - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

$17 + 15 y = - 2 \cdot - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

$17 + 15 y = - 2 \cdot - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

$17 + 15 y = - 2 \cdot - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Simplify the right side.

Multiply $- 2$ by $- 1$ .

$17 + 15 y = 2$

$x = \frac{17}{2} + \frac{9 y}{2}$

$17 + 15 y = 2$

$x = \frac{17}{2} + \frac{9 y}{2}$

$17 + 15 y = 2$

$x = \frac{17}{2} + \frac{9 y}{2}$

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

Subtract $17$ from both sides of the equation.

$15 y = 2 - 17$

$x = \frac{17}{2} + \frac{9 y}{2}$

Subtract $17$ from $2$ .

$15 y = - 15$

$x = \frac{17}{2} + \frac{9 y}{2}$

$15 y = - 15$

$x = \frac{17}{2} + \frac{9 y}{2}$

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

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

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

$x = \frac{17}{2} + \frac{9 y}{2}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

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

$x = \frac{17}{2} + \frac{9 y}{2}$

Divide $y$ by $1$ .

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

$x = \frac{17}{2} + \frac{9 y}{2}$

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

$x = \frac{17}{2} + \frac{9 y}{2}$

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

$x = \frac{17}{2} + \frac{9 y}{2}$

Simplify the right side.

Divide $- 15$ by $15$ .

$y = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

$y = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

$y = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

$y = - 1$

$x = \frac{17}{2} + \frac{9 y}{2}$

Step 4

Replace all occurrences of $y$ with $- 1$ in each equation.

Replace all occurrences of $y$ in $x = \frac{17}{2} + \frac{9 y}{2}$ with $- 1$ .

$x = \frac{17}{2} + \frac{9 (- 1)}{2}$

$y = - 1$

Simplify the right side.

Simplify $\frac{17}{2} + \frac{9 (- 1)}{2}$ .

Combine the numerators over the common denominator.

$x = \frac{17 + 9 (- 1)}{2}$

$y = - 1$

Simplify the expression.

Multiply $9$ by $- 1$ .

$x = \frac{17 - 9}{2}$

$y = - 1$

Subtract $9$ from $17$ .

$x = \frac{8}{2}$

$y = - 1$

Divide $8$ by $2$ .

$x = 4$

$y = - 1$

$x = 4$

$y = - 1$

$x = 4$

$y = - 1$

$x = 4$

$y = - 1$

$x = 4$

$y = - 1$

Step 5

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

$(4, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, - 1)$

Equation Form:

$x = 4, y = - 1$

Step 7

Solve the System of Equations -2x+9y=-17 -x-3y=-1

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