Solve by Substitution y=2x+1 y=-x-2

$y = 2 x + 1$ $y = - x - 2$

Step 1

Eliminate the equal sides of each equation and combine.

$2 x + 1 = - x - 2$

Step 2

Solve $2 x + 1 = - x - 2$ for $x$ .

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

Add $x$ to both sides of the equation.

$2 x + 1 + x = - 2$

Add $2 x$ and $x$ .

$3 x + 1 = - 2$

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

Subtract $1$ from both sides of the equation.

$3 x = - 2 - 1$

Subtract $1$ from $- 2$ .

$3 x = - 3$

Divide each term in $3 x = - 3$ by $3$ and simplify.

Divide each term in $3 x = - 3$ by $3$ .

$\frac{3 x}{3} = \frac{- 3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 3}{3}$

Divide $x$ by $1$ .

$x = \frac{- 3}{3}$

Simplify the right side.

Divide $- 3$ by $3$ .

$x = - 1$

Step 3

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 $1$ .

$y = - 1$

Step 4

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

$(- 1, - 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 1, - 1)$

Equation Form:

$x = - 1, y = - 1$

Step 6

Solve by Substitution y=2x+1 y=-x-2

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