Solve the System of @WORD y=-x-1 , y=2x+4

$y = - x - 1$ , $y = 2 x + 4$

Step 1

Eliminate the equal sides of each equation and combine.

$- x - 1 = 2 x + 4$

Step 2

Solve $- x - 1 = 2 x + 4$ for $x$ .

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

Subtract $2 x$ from both sides of the equation.

$- x - 1 - 2 x = 4$

Subtract $2 x$ from $- x$ .

$- 3 x - 1 = 4$

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

Add $1$ to both sides of the equation.

$- 3 x = 4 + 1$

Add $4$ and $1$ .

$- 3 x = 5$

Divide each term in $- 3 x = 5$ by $- 3$ and simplify.

Divide each term in $- 3 x = 5$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{5}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{5}{- 3}$

Divide $x$ by $1$ .

$x = \frac{5}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{3}$

Step 3

Evaluate $y$ when $x = - \frac{5}{3}$ .

Substitute $- \frac{5}{3}$ for $x$ .

$y = 2 (- \frac{5}{3}) + 4$

Simplify $2 (- \frac{5}{3}) + 4$ .

Simplify each term.

Multiply $2 (- \frac{5}{3})$ .

Multiply $- 1$ by $2$ .

$y = - 2 (\frac{5}{3}) + 4$

Combine $- 2$ and $\frac{5}{3}$ .

$y = \frac{- 2 \cdot 5}{3} + 4$

Multiply $- 2$ by $5$ .

$y = \frac{- 10}{3} + 4$

Move the negative in front of the fraction.

$y = - \frac{10}{3} + 4$

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{10}{3} + 4 \cdot \frac{3}{3}$

Combine $4$ and $\frac{3}{3}$ .

$y = - \frac{10}{3} + \frac{4 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = \frac{- 10 + 4 \cdot 3}{3}$

Simplify the numerator.

Multiply $4$ by $3$ .

$y = \frac{- 10 + 12}{3}$

Add $- 10$ and $12$ .

$y = \frac{2}{3}$

Step 4

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

$(- \frac{5}{3}, \frac{2}{3})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- \frac{5}{3}, \frac{2}{3})$

Equation Form:

$x = - \frac{5}{3}, y = \frac{2}{3}$

Step 6

Solve the System of @WORD y=-x-1 , y=2x+4

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