Algebra Examples

$\frac{1}{2} x + y = - 4$ $y = 2 x + 16$

Step 1

Replace all occurrences of $y$ with $2 x + 16$ in each equation.

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Step 1.1

Replace all occurrences of $y$ in $\frac{1}{2} x + y = - 4$ with $2 x + 16$ .

$\frac{1}{2} x + 2 x + 16 = - 4$

$y = 2 x + 16$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $\frac{1}{2} x + 2 x + 16$ .

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Step 1.2.1.1

Remove parentheses.

$\frac{1}{2} x + 2 x + 16 = - 4$

$y = 2 x + 16$

Step 1.2.1.2

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

$\frac{x}{2} + 2 x + 16 = - 4$

$y = 2 x + 16$

Step 1.2.1.3

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

$\frac{x}{2} + 2 x \cdot \frac{2}{2} + 16 = - 4$

$y = 2 x + 16$

Step 1.2.1.4

Simplify terms.

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Step 1.2.1.4.1

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

$\frac{x}{2} + \frac{2 x \cdot 2}{2} + 16 = - 4$

$y = 2 x + 16$

Step 1.2.1.4.2

Combine the numerators over the common denominator.

$\frac{x + 2 x \cdot 2}{2} + 16 = - 4$

$y = 2 x + 16$

$\frac{x + 2 x \cdot 2}{2} + 16 = - 4$

$y = 2 x + 16$

Step 1.2.1.5

Simplify each term.

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Step 1.2.1.5.1

Simplify the numerator.

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Step 1.2.1.5.1.1

Factor $x$ out of $x + 2 x \cdot 2$ .

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Step 1.2.1.5.1.1.1

Raise $x$ to the power of $1$ .

$\frac{x + 2 x \cdot 2}{2} + 16 = - 4$

$y = 2 x + 16$

Step 1.2.1.5.1.1.2

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 + 2 x \cdot 2}{2} + 16 = - 4$

$y = 2 x + 16$

Step 1.2.1.5.1.1.3

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

$\frac{x \cdot 1 + x (2 \cdot 2)}{2} + 16 = - 4$

$y = 2 x + 16$

Step 1.2.1.5.1.1.4

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

$\frac{x (1 + 2 \cdot 2)}{2} + 16 = - 4$

$y = 2 x + 16$

$\frac{x (1 + 2 \cdot 2)}{2} + 16 = - 4$

$y = 2 x + 16$

Step 1.2.1.5.1.2

Multiply $2$ by $2$ .

$\frac{x (1 + 4)}{2} + 16 = - 4$

$y = 2 x + 16$

Step 1.2.1.5.1.3

Add $1$ and $4$ .

$\frac{x \cdot 5}{2} + 16 = - 4$

$y = 2 x + 16$

$\frac{x \cdot 5}{2} + 16 = - 4$

$y = 2 x + 16$

Step 1.2.1.5.2

Move $5$ to the left of $x$ .

$\frac{5 x}{2} + 16 = - 4$

$y = 2 x + 16$

$\frac{5 x}{2} + 16 = - 4$

$y = 2 x + 16$

$\frac{5 x}{2} + 16 = - 4$

$y = 2 x + 16$

$\frac{5 x}{2} + 16 = - 4$

$y = 2 x + 16$

$\frac{5 x}{2} + 16 = - 4$

$y = 2 x + 16$

Step 2

Solve for $x$ in $\frac{5 x}{2} + 16 = - 4$ .

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Step 2.1

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1.1

Subtract $16$ from both sides of the equation.

$\frac{5 x}{2} = - 4 - 16$

$y = 2 x + 16$

Step 2.1.2

Subtract $16$ from $- 4$ .

$\frac{5 x}{2} = - 20$

$y = 2 x + 16$

$\frac{5 x}{2} = - 20$

$y = 2 x + 16$

Step 2.2

Multiply both sides of the equation by $\frac{2}{5}$ .

$\frac{2}{5} \cdot \frac{5 x}{2} = \frac{2}{5} \cdot - 20$

$y = 2 x + 16$

Step 2.3

Simplify both sides of the equation.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Simplify $\frac{2}{5} \cdot \frac{5 x}{2}$ .

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Step 2.3.1.1.1

Cancel the common factor of $2$ .

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Step 2.3.1.1.1.1

Cancel the common factor.

$\frac{2}{5} \cdot \frac{5 x}{2} = \frac{2}{5} \cdot - 20$

$y = 2 x + 16$

Step 2.3.1.1.1.2

Rewrite the expression.

$\frac{1}{5} \cdot (5 x) = \frac{2}{5} \cdot - 20$

$y = 2 x + 16$

$\frac{1}{5} \cdot (5 x) = \frac{2}{5} \cdot - 20$

$y = 2 x + 16$

Step 2.3.1.1.2

Cancel the common factor of $5$ .

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Step 2.3.1.1.2.1

Factor $5$ out of $5 x$ .

$\frac{1}{5} \cdot (5 (x)) = \frac{2}{5} \cdot - 20$

$y = 2 x + 16$

Step 2.3.1.1.2.2

Cancel the common factor.

$\frac{1}{5} \cdot (5 x) = \frac{2}{5} \cdot - 20$

$y = 2 x + 16$

Step 2.3.1.1.2.3

Rewrite the expression.

$x = \frac{2}{5} \cdot - 20$

$y = 2 x + 16$

$x = \frac{2}{5} \cdot - 20$

$y = 2 x + 16$

$x = \frac{2}{5} \cdot - 20$

$y = 2 x + 16$

$x = \frac{2}{5} \cdot - 20$

$y = 2 x + 16$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Simplify $\frac{2}{5} \cdot - 20$ .

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Step 2.3.2.1.1

Cancel the common factor of $5$ .

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Step 2.3.2.1.1.1

Factor $5$ out of $- 20$ .

$x = \frac{2}{5} \cdot (5 (- 4))$

$y = 2 x + 16$

Step 2.3.2.1.1.2

Cancel the common factor.

$x = \frac{2}{5} \cdot (5 \cdot - 4)$

$y = 2 x + 16$

Step 2.3.2.1.1.3

Rewrite the expression.

$x = 2 \cdot - 4$

$y = 2 x + 16$

$x = 2 \cdot - 4$

$y = 2 x + 16$

Step 2.3.2.1.2

Multiply $2$ by $- 4$ .

$x = - 8$

$y = 2 x + 16$

$x = - 8$

$y = 2 x + 16$

$x = - 8$

$y = 2 x + 16$

$x = - 8$

$y = 2 x + 16$

$x = - 8$

$y = 2 x + 16$

Step 3

Replace all occurrences of $x$ with $- 8$ in each equation.

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Step 3.1

Replace all occurrences of $x$ in $y = 2 x + 16$ with $- 8$ .

$y = 2 (- 8) + 16$

$x = - 8$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $2 (- 8) + 16$ .

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Step 3.2.1.1

Multiply $2$ by $- 8$ .

$y = - 16 + 16$

$x = - 8$

Step 3.2.1.2

Add $- 16$ and $16$ .

$y = 0$

$x = - 8$

$y = 0$

$x = - 8$

$y = 0$

$x = - 8$

$y = 0$

$x = - 8$

Step 4

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

$(- 8, 0)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 8, 0)$

Equation Form:

$x = - 8, y = 0$

Step 6