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

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

Eliminate the equal sides of each equation and combine.

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

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

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

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

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

Subtract $\frac{3 x}{2}$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

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

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

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

Factor $x$ out of $- 3 x$ .

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

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

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

Multiply $- 1$ by $2$ .

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

Subtract $3$ from $- 2$ .

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

Move $- 5$ to the left of $x$ .

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

Move the negative in front of the fraction.

$- \frac{5 x}{2} + 3 = - 2$

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

Subtract $3$ from both sides of the equation.

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

Subtract $3$ from $- 2$ .

$- \frac{5 x}{2} = - 5$

Multiply both sides of the equation by $- \frac{2}{5}$ .

$- \frac{2}{5} (- \frac{5 x}{2}) = - \frac{2}{5} \cdot - 5$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{5} (- \frac{5 x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{- 2}{5} (- \frac{5 x}{2}) = - \frac{2}{5} \cdot - 5$

Move the leading negative in $- \frac{5 x}{2}$ into the numerator.

$\frac{- 2}{5} \cdot \frac{- 5 x}{2} = - \frac{2}{5} \cdot - 5$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{5} \cdot \frac{- 5 x}{2} = - \frac{2}{5} \cdot - 5$

Cancel the common factor.

$\frac{2 \cdot - 1}{5} \cdot \frac{- 5 x}{2} = - \frac{2}{5} \cdot - 5$

Rewrite the expression.

$\frac{- 1}{5} (- 5 x) = - \frac{2}{5} \cdot - 5$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5 x$ .

$\frac{- 1}{5} (5 (- x)) = - \frac{2}{5} \cdot - 5$

Cancel the common factor.

$\frac{- 1}{5} (5 (- x)) = - \frac{2}{5} \cdot - 5$

Rewrite the expression.

$- - x = - \frac{2}{5} \cdot - 5$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{5} \cdot - 5$

Multiply $x$ by $1$ .

$x = - \frac{2}{5} \cdot - 5$

Simplify the right side.

Simplify $- \frac{2}{5} \cdot - 5$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$x = \frac{- 2}{5} \cdot - 5$

Factor $5$ out of $- 5$ .

$x = \frac{- 2}{5} \cdot (5 (- 1))$

Cancel the common factor.

$x = \frac{- 2}{5} \cdot (5 \cdot - 1)$

Rewrite the expression.

$x = - 2 \cdot - 1$

Multiply $- 2$ by $- 1$ .

$x = 2$

Evaluate $y$ when $x = 2$ .

Substitute $2$ for $x$ .

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

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

Multiply $\frac{3}{2}$ by $2$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$y = 3 - 2$

Subtract $2$ from $3$ .

$y = 1$

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

$(2, 1)$

The result can be shown in multiple forms.

Point Form:

$(2, 1)$

Equation Form:

$x = 2, y = 1$

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

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