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

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

Step 1

Eliminate the equal sides of each equation and combine.

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

Step 2

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

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

$- \frac{x}{2} - 2 = - \frac{3}{2} x + 2$

Simplify each term.

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

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

Move $3$ to the left of $x$ .

$- \frac{x}{2} - 2 = - \frac{3 x}{2} + 2$

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

Add $\frac{3 x}{2}$ to both sides of the equation.

$- \frac{x}{2} - 2 + \frac{3 x}{2} = 2$

Combine the numerators over the common denominator.

$- 2 + \frac{- x + 3 x}{2} = 2$

Add $- x$ and $3 x$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

$- 2 + x = 2$

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

Add $2$ to both sides of the equation.

$x = 2 + 2$

Add $2$ and $2$ .

$x = 4$

Step 3

Evaluate $y$ when $x = 4$ .

Substitute $4$ for $x$ .

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

Substitute $4$ for $x$ in $y = - \frac{3}{2} \cdot 4 + 2$ and solve for $y$ .

Remove parentheses.

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

Simplify $- \frac{3}{2} \cdot 4 + 2$ .

Simplify each term.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

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

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = - 3 \cdot 2 + 2$

Multiply $- 3$ by $2$ .

$y = - 6 + 2$

Add $- 6$ and $2$ .

$y = - 4$

Step 4

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

$(4, - 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, - 4)$

Equation Form:

$x = 4, y = - 4$

Step 6

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

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