Algebra Examples

$x + 2 y = - 8$ $y = - \frac{3}{2} x - 6$

Step 1

Subtract $2 y$ from both sides of the equation.

$x = - 8 - 2 y$

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

Step 2

Replace all occurrences of $x$ with $- 8 - 2 y$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $y = - \frac{3}{2} x - 6$ with $- 8 - 2 y$ .

$y = - \frac{3}{2} \cdot (- 8 - 2 y) - 6$

$x = - 8 - 2 y$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Simplify $- \frac{3}{2} \cdot (- 8 - 2 y) - 6$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

$y = - \frac{3}{2} \cdot - 8 - \frac{3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.2.1

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

$y = \frac{- 3}{2} \cdot - 8 - \frac{3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

Step 2.2.1.1.2.2

Factor $2$ out of $- 8$ .

$y = \frac{- 3}{2} \cdot (2 (- 4)) - \frac{3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

Step 2.2.1.1.2.3

Cancel the common factor.

$y = \frac{- 3}{2} \cdot (2 \cdot - 4) - \frac{3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

Step 2.2.1.1.2.4

Rewrite the expression.

$y = - 3 \cdot - 4 - \frac{3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

$y = - 3 \cdot - 4 - \frac{3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

Step 2.2.1.1.3

Multiply $- 3$ by $- 4$ .

$y = 12 - \frac{3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

Step 2.2.1.1.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.4.1

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

$y = 12 + \frac{- 3}{2} \cdot (- 2 y) - 6$

$x = - 8 - 2 y$

Step 2.2.1.1.4.2

Factor $2$ out of $- 2 y$ .

$y = 12 + \frac{- 3}{2} \cdot (2 (- y)) - 6$

$x = - 8 - 2 y$

Step 2.2.1.1.4.3

Cancel the common factor.

$y = 12 + \frac{- 3}{2} \cdot (2 (- y)) - 6$

$x = - 8 - 2 y$

Step 2.2.1.1.4.4

Rewrite the expression.

$y = 12 - 3 (- y) - 6$

$x = - 8 - 2 y$

$y = 12 - 3 (- y) - 6$

$x = - 8 - 2 y$

Step 2.2.1.1.5

Multiply $- 1$ by $- 3$ .

$y = 12 + 3 y - 6$

$x = - 8 - 2 y$

$y = 12 + 3 y - 6$

$x = - 8 - 2 y$

Step 2.2.1.2

Subtract $6$ from $12$ .

$y = 3 y + 6$

$x = - 8 - 2 y$

$y = 3 y + 6$

$x = - 8 - 2 y$

$y = 3 y + 6$

$x = - 8 - 2 y$

$y = 3 y + 6$

$x = - 8 - 2 y$

Step 3

Solve for $y$ in $y = 3 y + 6$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

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

$y - 3 y = 6$

$x = - 8 - 2 y$

Step 3.1.2

Subtract $3 y$ from $y$ .

$- 2 y = 6$

$x = - 8 - 2 y$

$- 2 y = 6$

$x = - 8 - 2 y$

Step 3.2

Divide each term in $- 2 y = 6$ by $- 2$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $- 2 y = 6$ by $- 2$ .

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

$x = - 8 - 2 y$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $- 2$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

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

$x = - 8 - 2 y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

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

$x = - 8 - 2 y$

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

$x = - 8 - 2 y$

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

$x = - 8 - 2 y$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Divide $6$ by $- 2$ .

$y = - 3$

$x = - 8 - 2 y$

$y = - 3$

$x = - 8 - 2 y$

$y = - 3$

$x = - 8 - 2 y$

$y = - 3$

$x = - 8 - 2 y$

Step 4

Replace all occurrences of $y$ with $- 3$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of $y$ in $x = - 8 - 2 y$ with $- 3$ .

$x = - 8 - 2 \cdot - 3$

$y = - 3$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $- 8 - 2 \cdot - 3$ .

Tap for more steps...

Step 4.2.1.1

Multiply $- 2$ by $- 3$ .

$x = - 8 + 6$

$y = - 3$

Step 4.2.1.2

Add $- 8$ and $6$ .

$x = - 2$

$y = - 3$

$x = - 2$

$y = - 3$

$x = - 2$

$y = - 3$

$x = - 2$

$y = - 3$

Step 5

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

$(- 2, - 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 2, - 3)$

Equation Form:

$x = - 2, y = - 3$

Step 7