Algebra Examples

$y = \frac{1}{2} x + 3$ $x - 2 y = - 6$

Step 1

Combine $\frac{1}{2}$ and $x$ .

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

$x - 2 y = - 6$

Step 2

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

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Step 2.1

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

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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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.

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

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

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Factor $2$ out of $- 2$ .

$x + 2 (- 1) (\frac{x}{2}) - 2 \cdot 3 = - 6$

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

Step 2.2.1.1.2.2

Cancel the common factor.

$x + 2 \cdot (- 1 \frac{x}{2}) - 2 \cdot 3 = - 6$

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

Step 2.2.1.1.2.3

Rewrite the expression.

$x - 1 x - 2 \cdot 3 = - 6$

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

$x - 1 x - 2 \cdot 3 = - 6$

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

Step 2.2.1.1.3

Multiply $- 2$ by $3$ .

$x - 1 x - 6 = - 6$

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

Step 2.2.1.1.4

Rewrite $- 1 x$ as $- x$ .

$x - x - 6 = - 6$

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

$x - x - 6 = - 6$

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

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Subtract $x$ from $x$ .

$0 - 6 = - 6$

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

Step 2.2.1.2.2

Subtract $6$ from $0$ .

$- 6 = - 6$

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

$- 6 = - 6$

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

$- 6 = - 6$

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

$- 6 = - 6$

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

$- 6 = - 6$

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

Step 3

Remove any equations from the system that are always true.

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

Step 4