Algebra Examples

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

Step 1

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

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Step 1.1

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

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

$x = - 2$

Step 1.2

Simplify the right side.

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Step 1.2.1

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

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Multiply $\frac{2}{3} (- 2)$ .

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Step 1.2.1.1.1.1

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

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

$x = - 2$

Step 1.2.1.1.1.2

Multiply $2$ by $- 2$ .

$y = \frac{- 4}{3} + 3$

$x = - 2$

$y = \frac{- 4}{3} + 3$

$x = - 2$

Step 1.2.1.1.2

Move the negative in front of the fraction.

$y = - \frac{4}{3} + 3$

$x = - 2$

$y = - \frac{4}{3} + 3$

$x = - 2$

Step 1.2.1.2

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

$y = - \frac{4}{3} + 3 \cdot \frac{3}{3}$

$x = - 2$

Step 1.2.1.3

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

$y = - \frac{4}{3} + \frac{3 \cdot 3}{3}$

$x = - 2$

Step 1.2.1.4

Combine the numerators over the common denominator.

$y = \frac{- 4 + 3 \cdot 3}{3}$

$x = - 2$

Step 1.2.1.5

Simplify the numerator.

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Step 1.2.1.5.1

Multiply $3$ by $3$ .

$y = \frac{- 4 + 9}{3}$

$x = - 2$

Step 1.2.1.5.2

Add $- 4$ and $9$ .

$y = \frac{5}{3}$

$x = - 2$

$y = \frac{5}{3}$

$x = - 2$

$y = \frac{5}{3}$

$x = - 2$

$y = \frac{5}{3}$

$x = - 2$

$y = \frac{5}{3}$

$x = - 2$

Step 2

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

$(- 2, \frac{5}{3})$

Step 3

The result can be shown in multiple forms.

Point Form:

$(- 2, \frac{5}{3})$

Equation Form:

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

Step 4