Solve the System of Equations -4x+y=23 4x-9y=-15

$- 4 x + y = 23$ $4 x - 9 y = - 15$

Add $4 x$ to both sides of the equation.

$y = 23 + 4 x$

$4 x - 9 y = - 15$

Replace all occurrences of $y$ with $23 + 4 x$ in each equation.

Replace all occurrences of $y$ in $4 x - 9 y = - 15$ with $23 + 4 x$ .

$4 x - 9 (23 + 4 x) = - 15$

$y = 23 + 4 x$

Simplify the left side.

Simplify $4 x - 9 (23 + 4 x)$ .

Simplify each term.

Apply the distributive property.

$4 x - 9 \cdot 23 - 9 (4 x) = - 15$

$y = 23 + 4 x$

Multiply $- 9$ by $23$ .

$4 x - 207 - 9 (4 x) = - 15$

$y = 23 + 4 x$

Multiply $4$ by $- 9$ .

$4 x - 207 - 36 x = - 15$

$y = 23 + 4 x$

$4 x - 207 - 36 x = - 15$

$y = 23 + 4 x$

Subtract $36 x$ from $4 x$ .

$- 32 x - 207 = - 15$

$y = 23 + 4 x$

$- 32 x - 207 = - 15$

$y = 23 + 4 x$

$- 32 x - 207 = - 15$

$y = 23 + 4 x$

$- 32 x - 207 = - 15$

$y = 23 + 4 x$

Solve for $x$ in $- 32 x - 207 = - 15$ .

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

Add $207$ to both sides of the equation.

$- 32 x = - 15 + 207$

$y = 23 + 4 x$

Add $- 15$ and $207$ .

$- 32 x = 192$

$y = 23 + 4 x$

$- 32 x = 192$

$y = 23 + 4 x$

Divide each term in $- 32 x = 192$ by $- 32$ and simplify.

Divide each term in $- 32 x = 192$ by $- 32$ .

$\frac{- 32 x}{- 32} = \frac{192}{- 32}$

$y = 23 + 4 x$

Simplify the left side.

Cancel the common factor of $- 32$ .

Cancel the common factor.

$\frac{- 32 x}{- 32} = \frac{192}{- 32}$

$y = 23 + 4 x$

Divide $x$ by $1$ .

$x = \frac{192}{- 32}$

$y = 23 + 4 x$

$x = \frac{192}{- 32}$

$y = 23 + 4 x$

$x = \frac{192}{- 32}$

$y = 23 + 4 x$

Simplify the right side.

Divide $192$ by $- 32$ .

$x = - 6$

$y = 23 + 4 x$

$x = - 6$

$y = 23 + 4 x$

$x = - 6$

$y = 23 + 4 x$

$x = - 6$

$y = 23 + 4 x$

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

Replace all occurrences of $x$ in $y = 23 + 4 x$ with $- 6$ .

$y = 23 + 4 (- 6)$

$x = - 6$

Simplify the right side.

Simplify $23 + 4 (- 6)$ .

Multiply $4$ by $- 6$ .

$y = 23 - 24$

$x = - 6$

Subtract $24$ from $23$ .

$y = - 1$

$x = - 6$

$y = - 1$

$x = - 6$

$y = - 1$

$x = - 6$

$y = - 1$

$x = - 6$

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

$(- 6, - 1)$

The result can be shown in multiple forms.

Point Form:

$(- 6, - 1)$

Equation Form:

$x = - 6, y = - 1$

Solve the System of Equations -4x+y=23 4x-9y=-15

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