Solve the System of Equations y=-7x+3 y=-x-3

$y = - 7 x + 3$ $y = - x - 3$

Eliminate the equal sides of each equation and combine.

$- 7 x + 3 = - x - 3$

Solve $- 7 x + 3 = - x - 3$ for $x$ .

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

Add $x$ to both sides of the equation.

$- 7 x + 3 + x = - 3$

Add $- 7 x$ and $x$ .

$- 6 x + 3 = - 3$

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

Subtract $3$ from both sides of the equation.

$- 6 x = - 3 - 3$

Subtract $3$ from $- 3$ .

$- 6 x = - 6$

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 $- 6$ .

$x = 1$

Evaluate $y$ when $x = 1$ .

Substitute $1$ for $x$ .

$y = - (1) - 3$

Simplify $- (1) - 3$ .

Multiply $- 1$ by $1$ .

$y = - 1 - 3$

Subtract $3$ from $- 1$ .

$y = - 4$

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

$(1, - 4)$

The result can be shown in multiple forms.

Point Form:

$(1, - 4)$

Equation Form:

$x = 1, y = - 4$