Solve the System of Equations 9x+y=2 -4x-y=-17

$9 x + y = 2$ $- 4 x - y = - 17$

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

$y = 2 - 9 x$

$- 4 x - y = - 17$

Replace all occurrences of $y$ with $2 - 9 x$ in each equation.

Replace all occurrences of $y$ in $- 4 x - y = - 17$ with $2 - 9 x$ .

$- 4 x - (2 - 9 x) = - 17$

$y = 2 - 9 x$

Simplify the left side.

Simplify $- 4 x - (2 - 9 x)$ .

Simplify each term.

Apply the distributive property.

$- 4 x - 1 \cdot 2 - (- 9 x) = - 17$

$y = 2 - 9 x$

Multiply $- 1$ by $2$ .

$- 4 x - 2 - (- 9 x) = - 17$

$y = 2 - 9 x$

Multiply $- 9$ by $- 1$ .

$- 4 x - 2 + 9 x = - 17$

$y = 2 - 9 x$

$- 4 x - 2 + 9 x = - 17$

$y = 2 - 9 x$

Add $- 4 x$ and $9 x$ .

$5 x - 2 = - 17$

$y = 2 - 9 x$

$5 x - 2 = - 17$

$y = 2 - 9 x$

$5 x - 2 = - 17$

$y = 2 - 9 x$

$5 x - 2 = - 17$

$y = 2 - 9 x$

Solve for $x$ in $5 x - 2 = - 17$ .

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

Add $2$ to both sides of the equation.

$5 x = - 17 + 2$

$y = 2 - 9 x$

Add $- 17$ and $2$ .

$5 x = - 15$

$y = 2 - 9 x$

$5 x = - 15$

$y = 2 - 9 x$

Divide each term in $5 x = - 15$ by $5$ and simplify.

Divide each term in $5 x = - 15$ by $5$ .

$\frac{5 x}{5} = \frac{- 15}{5}$

$y = 2 - 9 x$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 15}{5}$

$y = 2 - 9 x$

Divide $x$ by $1$ .

$x = \frac{- 15}{5}$

$y = 2 - 9 x$

$x = \frac{- 15}{5}$

$y = 2 - 9 x$

$x = \frac{- 15}{5}$

$y = 2 - 9 x$

Simplify the right side.

Divide $- 15$ by $5$ .

$x = - 3$

$y = 2 - 9 x$

$x = - 3$

$y = 2 - 9 x$

$x = - 3$

$y = 2 - 9 x$

$x = - 3$

$y = 2 - 9 x$

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

Replace all occurrences of $x$ in $y = 2 - 9 x$ with $- 3$ .

$y = 2 - 9 \cdot - 3$

$x = - 3$

Simplify the right side.

Simplify $2 - 9 \cdot - 3$ .

Multiply $- 9$ by $- 3$ .

$y = 2 + 27$

$x = - 3$

Add $2$ and $27$ .

$y = 29$

$x = - 3$

$y = 29$

$x = - 3$

$y = 29$

$x = - 3$

$y = 29$

$x = - 3$

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

$(- 3, 29)$

The result can be shown in multiple forms.

Point Form:

$(- 3, 29)$

Equation Form:

$x = - 3, y = 29$

Solve the System of Equations 9x+y=2 -4x-y=-17

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