Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

$2 x + 3 y = 6$

Step 1.2

Move $2$ to the left of $x$ .

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

$2 x + 3 y = 6$

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

$2 x + 3 y = 6$

Step 2

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

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Step 2.1

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

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

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

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

Step 2.2.1.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.1.2.1

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

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

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

Step 2.2.1.1.2.2

Cancel the common factor.

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

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

Step 2.2.1.1.2.3

Rewrite the expression.

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

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

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

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

Step 2.2.1.1.3

Multiply $3$ by $2$ .

$2 x - 2 x + 6 = 6$

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

$2 x - 2 x + 6 = 6$

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

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Subtract $2 x$ from $2 x$ .

$0 + 6 = 6$

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

Step 2.2.1.2.2

Add $0$ and $6$ .

$6 = 6$

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

$6 = 6$

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

$6 = 6$

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

$6 = 6$

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

$6 = 6$

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

Step 3

Remove any equations from the system that are always true.

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

Step 4