Solve the System of Equations y=3/2x-7 x+2y=-6

$y = \frac{3}{2} x - 7$ $x + 2 y = - 6$

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

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

$x + 2 y = - 6$

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

Replace all occurrences of $y$ in $x + 2 y = - 6$ with $\frac{3 x}{2} - 7$ .

$x + 2 (\frac{3 x}{2} - 7) = - 6$

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

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$x + 2 (\frac{3 x}{2}) + 2 \cdot - 7 = - 6$

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

Cancel the common factor of $2$ .

Cancel the common factor.

$x + 2 (\frac{3 x}{2}) + 2 \cdot - 7 = - 6$

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

Rewrite the expression.

$x + 3 x + 2 \cdot - 7 = - 6$

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

$x + 3 x + 2 \cdot - 7 = - 6$

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

Multiply $2$ by $- 7$ .

$x + 3 x - 14 = - 6$

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

$x + 3 x - 14 = - 6$

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

Add $x$ and $3 x$ .

$4 x - 14 = - 6$

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

$4 x - 14 = - 6$

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

$4 x - 14 = - 6$

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

$4 x - 14 = - 6$

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

Solve for $x$ in $4 x - 14 = - 6$ .

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

Add $14$ to both sides of the equation.

$4 x = - 6 + 14$

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

Add $- 6$ and $14$ .

$4 x = 8$

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

$4 x = 8$

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

Divide each term in $4 x = 8$ by $4$ and simplify.

Divide each term in $4 x = 8$ by $4$ .

$\frac{4 x}{4} = \frac{8}{4}$

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{8}{4}$

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

Divide $x$ by $1$ .

$x = \frac{8}{4}$

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

$x = \frac{8}{4}$

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

$x = \frac{8}{4}$

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

Simplify the right side.

Divide $8$ by $4$ .

$x = 2$

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

$x = 2$

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

$x = 2$

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

$x = 2$

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

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+2y=-6

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