Algebra Examples

$x - 2 y = - 4$ $y = \frac{1}{2} x + 2$

Step 1

Add $2 y$ to both sides of the equation.

$x = - 4 + 2 y$

$y = \frac{1}{2} x + 2$

Step 2

Replace all occurrences of $x$ with $- 4 + 2 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $y = \frac{1}{2} x + 2$ with $- 4 + 2 y$ .

$y = \frac{1}{2} \cdot (- 4 + 2 y) + 2$

$x = - 4 + 2 y$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{1}{2} \cdot (- 4 + 2 y) + 2$ .

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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.

$y = \frac{1}{2} \cdot - 4 + \frac{1}{2} \cdot (2 y) + 2$

$x = - 4 + 2 y$

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 $- 4$ .

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

$x = - 4 + 2 y$

Step 2.2.1.1.2.2

Cancel the common factor.

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

$x = - 4 + 2 y$

Step 2.2.1.1.2.3

Rewrite the expression.

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

$x = - 4 + 2 y$

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

$x = - 4 + 2 y$

Step 2.2.1.1.3

Cancel the common factor of $2$ .

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Step 2.2.1.1.3.1

Factor $2$ out of $2 y$ .

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

$x = - 4 + 2 y$

Step 2.2.1.1.3.2

Cancel the common factor.

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

$x = - 4 + 2 y$

Step 2.2.1.1.3.3

Rewrite the expression.

$y = - 2 + y + 2$

$x = - 4 + 2 y$

$y = - 2 + y + 2$

$x = - 4 + 2 y$

$y = - 2 + y + 2$

$x = - 4 + 2 y$

Step 2.2.1.2

Combine the opposite terms in $- 2 + y + 2$ .

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Step 2.2.1.2.1

Add $- 2$ and $2$ .

$y = y + 0$

$x = - 4 + 2 y$

Step 2.2.1.2.2

Add $y$ and $0$ .

$y = y$

$x = - 4 + 2 y$

$y = y$

$x = - 4 + 2 y$

$y = y$

$x = - 4 + 2 y$

$y = y$

$x = - 4 + 2 y$

$y = y$

$x = - 4 + 2 y$

Step 3

Remove any equations from the system that are always true.

$x = - 4 + 2 y$

Step 4