Algebra Examples

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 1

Replace all occurrences of

y

$y$ with

2 x + 16

$2 x + 16$ in each equation.

Tap for more steps...

Step 1.1

Replace all occurrences of

y

$y$ in

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

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

2 x + 16

$2 x + 16$ .

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Simplify

\frac{1}{2} x + 2 x + 16

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

Tap for more steps...

Step 1.2.1.1

Remove parentheses.

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 1.2.1.2

Combine

\frac{1}{2}

$\frac{1}{2}$ and

x

$x$ .

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 1.2.1.3

To write

2 x

$2 x$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 1.2.1.4

Simplify terms.

Tap for more steps...

Step 1.2.1.4.1

Combine

2 x

$2 x$ and

\frac{2}{2}

$\frac{2}{2}$ .

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 1.2.1.4.2

Combine the numerators over the common denominator.

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

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

y = 2 x + 16

$y = 2 x + 16$

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 1.2.1.5

Simplify each term.

Tap for more steps...

Step 1.2.1.5.1

Simplify the numerator.

Tap for more steps...

Step 1.2.1.5.1.1

Factor

x

$x$ out of

x + 2 x \cdot 2

$x + 2 x \cdot 2$ .

Tap for more steps...

Step 1.2.1.5.1.1.1

Raise

x

$x$ to the power of

1

$1$ .

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 1.2.1.5.1.1.2

Factor

x

$x$ out of

x^{1}

$x^{1}$ .

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 1.2.1.5.1.1.3

Factor

x

$x$ out of

2 x \cdot 2

$2 x \cdot 2$ .

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 1.2.1.5.1.1.4

Factor

x

$x$ out of

x \cdot 1 + x (2 \cdot 2)

$x \cdot 1 + x (2 \cdot 2)$ .

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

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

y = 2 x + 16

$y = 2 x + 16$

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 1.2.1.5.1.2

Multiply

2

$2$ by

2

$2$ .

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 1.2.1.5.1.3

Add

1

$1$ and

4

$4$ .

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

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

y = 2 x + 16

$y = 2 x + 16$

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 1.2.1.5.2

Move

5

$5$ to the left of

x

$x$ .

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

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

y = 2 x + 16

$y = 2 x + 16$

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

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

y = 2 x + 16

$y = 2 x + 16$

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

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

y = 2 x + 16

$y = 2 x + 16$

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

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

y = 2 x + 16

$y = 2 x + 16$

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 2

Solve for

x

$x$ in

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

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

Tap for more steps...

Step 2.1

Move all terms not containing

x

$x$ to the right side of the equation.

Tap for more steps...

Step 2.1.1

Subtract

16

$16$ from both sides of the equation.

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 2.1.2

Subtract

16

$16$ from

- 4

$- 4$ .

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

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

y = 2 x + 16

$y = 2 x + 16$

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 2.2

Multiply both sides of the equation by

\frac{2}{5}

$\frac{2}{5}$ .

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 2.3

Simplify both sides of the equation.

Tap for more steps...

Step 2.3.1

Simplify the left side.

Tap for more steps...

Step 2.3.1.1

Simplify

\frac{2}{5} \cdot \frac{5 x}{2}

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

Tap for more steps...

Step 2.3.1.1.1

Cancel the common factor of

2

$2$ .

Tap for more steps...

Step 2.3.1.1.1.1

Cancel the common factor.

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 2.3.1.1.1.2

Rewrite the expression.

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

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

y = 2 x + 16

$y = 2 x + 16$

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 2.3.1.1.2

Cancel the common factor of

5

$5$ .

Tap for more steps...

Step 2.3.1.1.2.1

Factor

5

$5$ out of

5 x

$5 x$ .

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 2.3.1.1.2.2

Cancel the common factor.

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 2.3.1.1.2.3

Rewrite the expression.

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

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

y = 2 x + 16

$y = 2 x + 16$

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

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

y = 2 x + 16

$y = 2 x + 16$

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

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

y = 2 x + 16

$y = 2 x + 16$

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 2.3.2

Simplify the right side.

Tap for more steps...

Step 2.3.2.1

Simplify

\frac{2}{5} \cdot - 20

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

Tap for more steps...

Step 2.3.2.1.1

Cancel the common factor of

5

$5$ .

Tap for more steps...

Step 2.3.2.1.1.1

Factor

5

$5$ out of

- 20

$- 20$ .

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 2.3.2.1.1.2

Cancel the common factor.

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

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

y = 2 x + 16

$y = 2 x + 16$

Step 2.3.2.1.1.3

Rewrite the expression.

x = 2 \cdot - 4

$x = 2 \cdot - 4$

y = 2 x + 16

$y = 2 x + 16$

x = 2 \cdot - 4

$x = 2 \cdot - 4$

y = 2 x + 16

$y = 2 x + 16$

Step 2.3.2.1.2

Multiply

2

$2$ by

- 4

$- 4$ .

x = - 8

$x = - 8$

y = 2 x + 16

$y = 2 x + 16$

x = - 8

$x = - 8$

y = 2 x + 16

$y = 2 x + 16$

x = - 8

$x = - 8$

y = 2 x + 16

$y = 2 x + 16$

x = - 8

$x = - 8$

y = 2 x + 16

$y = 2 x + 16$

x = - 8

$x = - 8$

y = 2 x + 16

$y = 2 x + 16$

Step 3

Replace all occurrences of

x

$x$ with

- 8

$- 8$ in each equation.

Tap for more steps...

Step 3.1

Replace all occurrences of

x

$x$ in

y = 2 x + 16

$y = 2 x + 16$ with

- 8

$- 8$ .

y = 2 (- 8) + 16

$y = 2 (- 8) + 16$

x = - 8

$x = - 8$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Simplify

2 (- 8) + 16

$2 (- 8) + 16$ .

Tap for more steps...

Step 3.2.1.1

Multiply

2

$2$ by

- 8

$- 8$ .

y = - 16 + 16

$y = - 16 + 16$

x = - 8

$x = - 8$

Step 3.2.1.2

Add

- 16

$- 16$ and

16

$16$ .

y = 0

$y = 0$

x = - 8

$x = - 8$

y = 0

$y = 0$

x = - 8

$x = - 8$

y = 0

$y = 0$

x = - 8

$x = - 8$

y = 0

$y = 0$

x = - 8

$x = - 8$

Step 4

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

(- 8, 0)

$(- 8, 0)$

Step 5

The result can be shown in multiple forms.

Point Form:

(- 8, 0)

$(- 8, 0)$

Equation Form:

x = - 8, y = 0

$x = - 8, y = 0$

Step 6