Solve the System of Equations y=5x y=9x+4

$y = 5 x$ $y = 9 x + 4$

Eliminate the equal sides of each equation and combine.

$5 x = 9 x + 4$

Solve $5 x = 9 x + 4$ for $x$ .

Move all terms containing $x$ to the left side of the equation.

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

$5 x - 9 x = 4$

Subtract $9 x$ from $5 x$ .

$- 4 x = 4$

Divide each term in $- 4 x = 4$ by $- 4$ and simplify.

Divide each term in $- 4 x = 4$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{4}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{4}{- 4}$

Divide $x$ by $1$ .

$x = \frac{4}{- 4}$

Simplify the right side.

Divide $4$ by $- 4$ .

$x = - 1$

Evaluate $y$ when $x = - 1$ .

Substitute $- 1$ for $x$ .

$y = 9 (- 1) + 4$

Simplify $9 (- 1) + 4$ .

Multiply $9$ by $- 1$ .

$y = - 9 + 4$

Add $- 9$ and $4$ .

$y = - 5$

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

$(- 1, - 5)$

The result can be shown in multiple forms.

Point Form:

$(- 1, - 5)$

Equation Form:

$x = - 1, y = - 5$