Solve the System of Equations y=-1/2x-1 y=3x-8

$y = - \frac{1}{2} x - 1$ $y = 3 x - 8$

Eliminate the equal sides of each equation and combine.

$- \frac{1}{2} x - 1 = 3 x - 8$

Solve $- \frac{1}{2} x - 1 = 3 x - 8$ for $x$ .

Combine $x$ and $\frac{1}{2}$ .

$- \frac{x}{2} - 1 = 3 x - 8$

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

Subtract $3 x$ from both sides of the equation.

$- \frac{x}{2} - 1 - 3 x = - 8$

To write $- 3 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{x}{2} - 3 x \cdot \frac{2}{2} - 1 = - 8$

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

$- \frac{x}{2} + \frac{- 3 x \cdot 2}{2} - 1 = - 8$

Combine the numerators over the common denominator.

$\frac{- x - 3 x \cdot 2}{2} - 1 = - 8$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- x - 3 x \cdot 2$ .

Factor $x$ out of $- x$ .

$\frac{x \cdot - 1 - 3 x \cdot 2}{2} - 1 = - 8$

Factor $x$ out of $- 3 x \cdot 2$ .

$\frac{x \cdot - 1 + x (- 3 \cdot 2)}{2} - 1 = - 8$

Factor $x$ out of $x \cdot - 1 + x (- 3 \cdot 2)$ .

$\frac{x (- 1 - 3 \cdot 2)}{2} - 1 = - 8$

Multiply $- 3$ by $2$ .

$\frac{x (- 1 - 6)}{2} - 1 = - 8$

Subtract $6$ from $- 1$ .

$\frac{x \cdot - 7}{2} - 1 = - 8$

Move $- 7$ to the left of $x$ .

$\frac{- 7 \cdot x}{2} - 1 = - 8$

Move the negative in front of the fraction.

$- \frac{7 x}{2} - 1 = - 8$

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

Add $1$ to both sides of the equation.

$- \frac{7 x}{2} = - 8 + 1$

Add $- 8$ and $1$ .

$- \frac{7 x}{2} = - 7$

Multiply both sides of the equation by $- \frac{2}{7}$ .

$- \frac{2}{7} (- \frac{7 x}{2}) = - \frac{2}{7} \cdot - 7$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{7} (- \frac{7 x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{7}$ into the numerator.

$\frac{- 2}{7} (- \frac{7 x}{2}) = - \frac{2}{7} \cdot - 7$

Move the leading negative in $- \frac{7 x}{2}$ into the numerator.

$\frac{- 2}{7} \cdot \frac{- 7 x}{2} = - \frac{2}{7} \cdot - 7$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{7} \cdot \frac{- 7 x}{2} = - \frac{2}{7} \cdot - 7$

Cancel the common factor.

$\frac{2 \cdot - 1}{7} \cdot \frac{- 7 x}{2} = - \frac{2}{7} \cdot - 7$

Rewrite the expression.

$\frac{- 1}{7} (- 7 x) = - \frac{2}{7} \cdot - 7$

Cancel the common factor of $7$ .

Factor $7$ out of $- 7 x$ .

$\frac{- 1}{7} (7 (- x)) = - \frac{2}{7} \cdot - 7$

Cancel the common factor.

$\frac{- 1}{7} (7 (- x)) = - \frac{2}{7} \cdot - 7$

Rewrite the expression.

$- - x = - \frac{2}{7} \cdot - 7$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{7} \cdot - 7$

Multiply $x$ by $1$ .

$x = - \frac{2}{7} \cdot - 7$

Simplify the right side.

Simplify $- \frac{2}{7} \cdot - 7$ .

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{2}{7}$ into the numerator.

$x = \frac{- 2}{7} \cdot - 7$

Factor $7$ out of $- 7$ .

$x = \frac{- 2}{7} \cdot (7 (- 1))$

Cancel the common factor.

$x = \frac{- 2}{7} \cdot (7 \cdot - 1)$

Rewrite the expression.

$x = - 2 \cdot - 1$

Multiply $- 2$ by $- 1$ .

$x = 2$

Evaluate $y$ when $x = 2$ .

Substitute $2$ for $x$ .

$y = 3 (2) - 8$

Simplify $3 (2) - 8$ .

Multiply $3$ by $2$ .

$y = 6 - 8$

Subtract $8$ from $6$ .

$y = - 2$

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

$(2, - 2)$

The result can be shown in multiple forms.

Point Form:

$(2, - 2)$

Equation Form:

$x = 2, y = - 2$

Solve the System of Equations y=-1/2x-1 y=3x-8

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