Solve the System of Equations -9x+2y=23 and -4x-y=-3

$- 9 x + 2 y = 23$ and $- 4 x - y = - 3$

Solve for $x$ in $- 9 x + 2 y = 23$ .

Subtract $2 y$ from both sides of the equation.

$- 9 x = 23 - 2 y$

$- 4 x - y = - 3$

Divide each term in $- 9 x = 23 - 2 y$ by $- 9$ and simplify.

Divide each term in $- 9 x = 23 - 2 y$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{23}{- 9} + \frac{- 2 y}{- 9}$

$- 4 x - y = - 3$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{23}{- 9} + \frac{- 2 y}{- 9}$

$- 4 x - y = - 3$

Divide $x$ by $1$ .

$x = \frac{23}{- 9} + \frac{- 2 y}{- 9}$

$- 4 x - y = - 3$

$x = \frac{23}{- 9} + \frac{- 2 y}{- 9}$

$- 4 x - y = - 3$

$x = \frac{23}{- 9} + \frac{- 2 y}{- 9}$

$- 4 x - y = - 3$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{23}{9} + \frac{- 2 y}{- 9}$

$- 4 x - y = - 3$

Dividing two negative values results in a positive value.

$x = - \frac{23}{9} + \frac{2 y}{9}$

$- 4 x - y = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$- 4 x - y = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$- 4 x - y = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$- 4 x - y = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$- 4 x - y = - 3$

Replace all occurrences of $x$ with $- \frac{23}{9} + \frac{2 y}{9}$ in each equation.

Replace all occurrences of $x$ in $- 4 x - y = - 3$ with $- \frac{23}{9} + \frac{2 y}{9}$ .

$- 4 (- \frac{23}{9} + \frac{2 y}{9}) - y = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Simplify the left side.

Simplify $- 4 (- \frac{23}{9} + \frac{2 y}{9}) - y$ .

Simplify each term.

Apply the distributive property.

$- 4 (- \frac{23}{9}) - 4 \frac{2 y}{9} - y = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Multiply $- 4 (- \frac{23}{9})$ .

Multiply $- 1$ by $- 4$ .

$4 (\frac{23}{9}) - 4 \frac{2 y}{9} - y = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Combine $4$ and $\frac{23}{9}$ .

$\frac{4 \cdot 23}{9} - 4 \frac{2 y}{9} - y = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Multiply $4$ by $23$ .

$\frac{92}{9} - 4 \frac{2 y}{9} - y = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$\frac{92}{9} - 4 \frac{2 y}{9} - y = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Multiply $- 4 \frac{2 y}{9}$ .

Combine $- 4$ and $\frac{2 y}{9}$ .

$\frac{92}{9} + \frac{- 4 (2 y)}{9} - y = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Multiply $2$ by $- 4$ .

$\frac{92}{9} + \frac{- 8 y}{9} - y = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$\frac{92}{9} + \frac{- 8 y}{9} - y = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Move the negative in front of the fraction.

$\frac{92}{9} - \frac{8 y}{9} - y = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$\frac{92}{9} - \frac{8 y}{9} - y = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

To write $- y$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{92}{9} - \frac{8 y}{9} - y \cdot \frac{9}{9} = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Combine $- y$ and $\frac{9}{9}$ .

$\frac{92}{9} - \frac{8 y}{9} + \frac{- y \cdot 9}{9} = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Combine the numerators over the common denominator.

$\frac{92}{9} + \frac{- 8 y - y \cdot 9}{9} = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Combine the numerators over the common denominator.

$\frac{92 - 8 y - y \cdot 9}{9} = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Multiply $9$ by $- 1$ .

$\frac{92 - 8 y - 9 y}{9} = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Subtract $9 y$ from $- 8 y$ .

$\frac{92 - 17 y}{9} = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$\frac{92 - 17 y}{9} = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$\frac{92 - 17 y}{9} = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$\frac{92 - 17 y}{9} = - 3$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Solve for $y$ in $\frac{92 - 17 y}{9} = - 3$ .

Multiply both sides by $9$ .

$\frac{92 - 17 y}{9} \cdot 9 = - 3 \cdot 9$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Simplify.

Simplify the left side.

Simplify $\frac{92 - 17 y}{9} \cdot 9$ .

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{92 - 17 y}{9} \cdot 9 = - 3 \cdot 9$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Rewrite the expression.

$92 - 17 y = - 3 \cdot 9$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$92 - 17 y = - 3 \cdot 9$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Reorder $92$ and $- 17 y$ .

$- 17 y + 92 = - 3 \cdot 9$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$- 17 y + 92 = - 3 \cdot 9$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$- 17 y + 92 = - 3 \cdot 9$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Simplify the right side.

Multiply $- 3$ by $9$ .

$- 17 y + 92 = - 27$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$- 17 y + 92 = - 27$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$- 17 y + 92 = - 27$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Solve for $y$ .

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

Subtract $92$ from both sides of the equation.

$- 17 y = - 27 - 92$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Subtract $92$ from $- 27$ .

$- 17 y = - 119$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$- 17 y = - 119$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Divide each term in $- 17 y = - 119$ by $- 17$ and simplify.

Divide each term in $- 17 y = - 119$ by $- 17$ .

$\frac{- 17 y}{- 17} = \frac{- 119}{- 17}$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Simplify the left side.

Cancel the common factor of $- 17$ .

Cancel the common factor.

$\frac{- 17 y}{- 17} = \frac{- 119}{- 17}$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Divide $y$ by $1$ .

$y = \frac{- 119}{- 17}$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$y = \frac{- 119}{- 17}$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$y = \frac{- 119}{- 17}$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Simplify the right side.

Divide $- 119$ by $- 17$ .

$y = 7$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$y = 7$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$y = 7$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$y = 7$

$x = - \frac{23}{9} + \frac{2 y}{9}$

$y = 7$

$x = - \frac{23}{9} + \frac{2 y}{9}$

Replace all occurrences of $y$ with $7$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{23}{9} + \frac{2 y}{9}$ with $7$ .

$x = - \frac{23}{9} + \frac{2 (7)}{9}$

$y = 7$

Simplify the right side.

Simplify $- \frac{23}{9} + \frac{2 (7)}{9}$ .

Combine the numerators over the common denominator.

$x = \frac{- 23 + 2 (7)}{9}$

$y = 7$

Simplify the expression.

Multiply $2$ by $7$ .

$x = \frac{- 23 + 14}{9}$

$y = 7$

Add $- 23$ and $14$ .

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

$y = 7$

Divide $- 9$ by $9$ .

$x = - 1$

$y = 7$

$x = - 1$

$y = 7$

$x = - 1$

$y = 7$

$x = - 1$

$y = 7$

$x = - 1$

$y = 7$

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

$(- 1, 7)$

The result can be shown in multiple forms.

Point Form:

$(- 1, 7)$

Equation Form:

$x = - 1, y = 7$

Solve the System of Equations -9x+2y=23 and -4x-y=-3

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