Algebra Examples

$2 x = - 1 - y$ , $2 y = 6 x + 5$

Step 1

Find the slope and y-intercept of the first equation.

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Step 1.1

Rewrite in slope-intercept form.

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Step 1.1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.1.2

Rewrite the equation as $- 1 - y = 2 x$ .

$- 1 - y = 2 x$

Step 1.1.3

Add $1$ to both sides of the equation.

$- y = 2 x + 1$

Step 1.1.4

Divide each term in $- y = 2 x + 1$ by $- 1$ and simplify.

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Step 1.1.4.1

Divide each term in $- y = 2 x + 1$ by $- 1$ .

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

Step 1.1.4.2

Simplify the left side.

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Step 1.1.4.2.1

Dividing two negative values results in a positive value.

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

Step 1.1.4.2.2

Divide $y$ by $1$ .

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

Step 1.1.4.3

Simplify the right side.

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Step 1.1.4.3.1

Simplify each term.

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Step 1.1.4.3.1.1

Move the negative one from the denominator of $\frac{2 x}{- 1}$ .

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

Step 1.1.4.3.1.2

Rewrite $- 1 \cdot (2 x)$ as $- (2 x)$ .

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

Step 1.1.4.3.1.3

Multiply $2$ by $- 1$ .

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

Step 1.1.4.3.1.4

Divide $1$ by $- 1$ .

$y = - 2 x - 1$

Step 1.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m_{1} = - 2$

$b = - 1$

$m_{1} = - 2$

$b = - 1$

Step 2

Find the slope and y-intercept of the second equation.

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Step 2.1

Rewrite in slope-intercept form.

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Step 2.1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.1.2

Divide each term in $2 y = 6 x + 5$ by $2$ and simplify.

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Step 2.1.2.1

Divide each term in $2 y = 6 x + 5$ by $2$ .

$\frac{2 y}{2} = \frac{6 x}{2} + \frac{5}{2}$

Step 2.1.2.2

Simplify the left side.

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Step 2.1.2.2.1

Cancel the common factor of $2$ .

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Step 2.1.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{6 x}{2} + \frac{5}{2}$

Step 2.1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{6 x}{2} + \frac{5}{2}$

Step 2.1.2.3

Simplify the right side.

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Step 2.1.2.3.1

Cancel the common factor of $6$ and $2$ .

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Step 2.1.2.3.1.1

Factor $2$ out of $6 x$ .

$y = \frac{2 (3 x)}{2} + \frac{5}{2}$

Step 2.1.2.3.1.2

Cancel the common factors.

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Step 2.1.2.3.1.2.1

Factor $2$ out of $2$ .

$y = \frac{2 (3 x)}{2 (1)} + \frac{5}{2}$

Step 2.1.2.3.1.2.2

Cancel the common factor.

$y = \frac{2 (3 x)}{2 \cdot 1} + \frac{5}{2}$

Step 2.1.2.3.1.2.3

Rewrite the expression.

$y = \frac{3 x}{1} + \frac{5}{2}$

Step 2.1.2.3.1.2.4

Divide $3 x$ by $1$ .

$y = 3 x + \frac{5}{2}$

Step 2.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m_{2} = 3$

$b = \frac{5}{2}$

$m_{2} = 3$

$b = \frac{5}{2}$

Step 3

Compare the slopes $m$ of the two equations.

$m_{1} = - 2, m_{2} = 3$

Step 4

Compare the two slopes in the decimal form. If the slopes are equal, then the lines are parallel. If the slopes are not equal, then the lines are not parallel.

$m_{1} = - 2, m_{2} = 3$

Step 5

The equations are not parallel because the slopes of the two lines are not equal.

Not Parallel

Step 6