Solve the System of Equations y=3/2x-7 x+y=-2

$y = \frac{3}{2} x - 7$ $x + y = - 2$

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

$y = \frac{3 x}{2} - 7$

$x + y = - 2$

Replace all occurrences of $y$ with $\frac{3 x}{2} - 7$ in each equation.

Replace all occurrences of $y$ in $x + y = - 2$ with $\frac{3 x}{2} - 7$ .

$x + \frac{3 x}{2} - 7 = - 2$

$y = \frac{3 x}{2} - 7$

Simplify the left side.

Simplify $x + \frac{3 x}{2} - 7$ .

Remove parentheses.

$x + \frac{3 x}{2} - 7 = - 2$

$y = \frac{3 x}{2} - 7$

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

$x \cdot \frac{2}{2} + \frac{3 x}{2} - 7 = - 2$

$y = \frac{3 x}{2} - 7$

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

$\frac{x \cdot 2}{2} + \frac{3 x}{2} - 7 = - 2$

$y = \frac{3 x}{2} - 7$

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + 3 x}{2} - 7 = - 2$

$y = \frac{3 x}{2} - 7$

Add $x \cdot 2$ and $3 x$ .

Reorder $x$ and $2$ .

$\frac{2 \cdot x + 3 x}{2} - 7 = - 2$

$y = \frac{3 x}{2} - 7$

Add $2 \cdot x$ and $3 x$ .

$\frac{5 \cdot x}{2} - 7 = - 2$

$y = \frac{3 x}{2} - 7$

$\frac{5 x}{2} - 7 = - 2$

$y = \frac{3 x}{2} - 7$

$\frac{5 x}{2} - 7 = - 2$

$y = \frac{3 x}{2} - 7$

$\frac{5 x}{2} - 7 = - 2$

$y = \frac{3 x}{2} - 7$

$\frac{5 x}{2} - 7 = - 2$

$y = \frac{3 x}{2} - 7$

Solve for $x$ in $\frac{5 x}{2} - 7 = - 2$ .

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

Add $7$ to both sides of the equation.

$\frac{5 x}{2} = - 2 + 7$

$y = \frac{3 x}{2} - 7$

Add $- 2$ and $7$ .

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

$y = \frac{3 x}{2} - 7$

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

$y = \frac{3 x}{2} - 7$

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

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

$y = \frac{3 x}{2} - 7$

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

$y = \frac{3 x}{2} - 7$

Rewrite the expression.

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

$y = \frac{3 x}{2} - 7$

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

$y = \frac{3 x}{2} - 7$

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

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

$y = \frac{3 x}{2} - 7$

Cancel the common factor.

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

$y = \frac{3 x}{2} - 7$

Rewrite the expression.

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

$y = \frac{3 x}{2} - 7$

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

$y = \frac{3 x}{2} - 7$

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

$y = \frac{3 x}{2} - 7$

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

$y = \frac{3 x}{2} - 7$

Simplify the right side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

$y = \frac{3 x}{2} - 7$

Rewrite the expression.

$x = 2$

$y = \frac{3 x}{2} - 7$

$x = 2$

$y = \frac{3 x}{2} - 7$

$x = 2$

$y = \frac{3 x}{2} - 7$

$x = 2$

$y = \frac{3 x}{2} - 7$

$x = 2$

$y = \frac{3 x}{2} - 7$

Replace all occurrences of $x$ with $2$ in each equation.

Replace all occurrences of $x$ in $y = \frac{3 x}{2} - 7$ with $2$ .

$y = \frac{3 (2)}{2} - 7$

$x = 2$

Simplify the right side.

Simplify $\frac{3 (2)}{2} - 7$ .

Multiply $3$ by $2$ .

$y = \frac{6}{2} - 7$

$x = 2$

Divide $6$ by $2$ .

$y = 3 - 7$

$x = 2$

Subtract $7$ from $3$ .

$y = - 4$

$x = 2$

$y = - 4$

$x = 2$

$y = - 4$

$x = 2$

$y = - 4$

$x = 2$

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

$(2, - 4)$

The result can be shown in multiple forms.

Point Form:

$(2, - 4)$

Equation Form:

$x = 2, y = - 4$

Solve the System of Equations y=3/2x-7 x+y=-2

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