Solve the System of Equations y=-5x y=x-6

$y = - 5 x$ $y = x - 6$

Step 1

Eliminate the equal sides of each equation and combine.

$- 5 x = x - 6$

Step 2

Solve $- 5 x = x - 6$ for $x$ .

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

Subtract $x$ from both sides of the equation.

$- 5 x - x = - 6$

Subtract $x$ from $- 5 x$ .

$- 6 x = - 6$

Divide each term in $- 6 x = - 6$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 6$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 6}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 6}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 6}$

Simplify the right side.

Divide $- 6$ by $- 6$ .

$x = 1$

Step 3

Evaluate $y$ when $x = 1$ .

Substitute $1$ for $x$ .

$y = (1) - 6$

Substitute $1$ for $x$ in $y = (1) - 6$ and solve for $y$ .

Remove parentheses.

$y = 1 - 6$

Remove parentheses.

$y = (1) - 6$

Subtract $6$ from $1$ .

$y = - 5$

Step 4

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

$(1, - 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, - 5)$

Equation Form:

$x = 1, y = - 5$

Step 6