Solve the System of Equations y=4x+3 and y=-x-2

$y = 4 x + 3$ and $y = - x - 2$

Eliminate the equal sides of each equation and combine.

$4 x + 3 = - x - 2$

Solve $4 x + 3 = - x - 2$ for $x$ .

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

Add $x$ to both sides of the equation.

$4 x + 3 + x = - 2$

Add $4 x$ and $x$ .

$5 x + 3 = - 2$

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

Subtract $3$ from both sides of the equation.

$5 x = - 2 - 3$

Subtract $3$ from $- 2$ .

$5 x = - 5$

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 5$ by $5$ .

$x = - 1$

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

Substitute $- 1$ for $x$ .

$y = - (- 1) - 2$

Simplify $- (- 1) - 2$ .

Multiply $- 1$ by $- 1$ .

$y = 1 - 2$

Subtract $2$ from $1$ .

$y = - 1$

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

$(- 1, - 1)$

The result can be shown in multiple forms.

Point Form:

$(- 1, - 1)$

Equation Form:

$x = - 1, y = - 1$