Algebra Examples

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

Step 1

Eliminate the equal sides of each equation and combine.

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

Step 2

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

Tap for more steps...

Step 2.1

Simplify $\frac{3}{2} x$ .

Tap for more steps...

Step 2.1.1

Rewrite.

$0 + 0 + \frac{3}{2} x = 3 x - 3$

Step 2.1.2

Simplify by adding zeros.

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

Step 2.1.3

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

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

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

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

Step 2.2.2

To write $- 3 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.2.3

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

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

Step 2.2.4

Combine the numerators over the common denominator.

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

Step 2.2.5

Simplify the numerator.

Tap for more steps...

Step 2.2.5.1

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

Tap for more steps...

Step 2.2.5.1.1

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

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

Step 2.2.5.1.2

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

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

Step 2.2.5.1.3

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

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

Step 2.2.5.2

Multiply $- 1$ by $2$ .

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

Step 2.2.5.3

Subtract $2$ from $1$ .

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

Step 2.2.5.4

Multiply $- 1$ by $3$ .

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

Step 2.2.6

Move the negative in front of the fraction.

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

Step 2.3

Multiply both sides of the equation by $- \frac{2}{3}$ .

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

Step 2.4

Simplify both sides of the equation.

Tap for more steps...

Step 2.4.1

Simplify the left side.

Tap for more steps...

Step 2.4.1.1

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

Tap for more steps...

Step 2.4.1.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.4.1.1.1.1

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

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

Step 2.4.1.1.1.2

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

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

Step 2.4.1.1.1.3

Factor $2$ out of $- 2$ .

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

Step 2.4.1.1.1.4

Cancel the common factor.

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

Step 2.4.1.1.1.5

Rewrite the expression.

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

Step 2.4.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.4.1.1.2.1

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

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

Step 2.4.1.1.2.2

Cancel the common factor.

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

Step 2.4.1.1.2.3

Rewrite the expression.

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

Step 2.4.1.1.3

Multiply.

Tap for more steps...

Step 2.4.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 2.4.1.1.3.2

Multiply $x$ by $1$ .

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

Step 2.4.2

Simplify the right side.

Tap for more steps...

Step 2.4.2.1

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

Tap for more steps...

Step 2.4.2.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.4.2.1.1.1

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

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

Step 2.4.2.1.1.2

Factor $3$ out of $- 3$ .

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

Step 2.4.2.1.1.3

Cancel the common factor.

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

Step 2.4.2.1.1.4

Rewrite the expression.

$x = - 2 \cdot - 1$

Step 2.4.2.1.2

Multiply $- 2$ by $- 1$ .

$x = 2$

Step 3

Evaluate $y$ when $x = 2$ .

Tap for more steps...

Step 3.1

Substitute $2$ for $x$ .

$y = 3 (2) - 3$

Step 3.2

Simplify $3 (2) - 3$ .

Tap for more steps...

Step 3.2.1

Multiply $3$ by $2$ .

$y = 6 - 3$

Step 3.2.2

Subtract $3$ from $6$ .

$y = 3$

Step 4

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

$(2, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 3)$

Equation Form:

$x = 2, y = 3$

Step 6