Finite Math Examples

$12 x - 3 y = 3$ , $y = 4 x - 1$

Step 1

Rewrite in slope-intercept form.

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Step 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 1.2

Subtract $12 x$ from both sides of the equation.

$- 3 y = 3 - 12 x$

Step 1.3

Divide each term in $- 3 y = 3 - 12 x$ by $- 3$ and simplify.

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Step 1.3.1

Divide each term in $- 3 y = 3 - 12 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{3}{- 3} + \frac{- 12 x}{- 3}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 3$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{3}{- 3} + \frac{- 12 x}{- 3}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{3}{- 3} + \frac{- 12 x}{- 3}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Divide $3$ by $- 3$ .

$y = - 1 + \frac{- 12 x}{- 3}$

Step 1.3.3.1.2

Cancel the common factor of $- 12$ and $- 3$ .

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Step 1.3.3.1.2.1

Factor $- 3$ out of $- 12 x$ .

$y = - 1 + \frac{- 3 (4 x)}{- 3}$

Step 1.3.3.1.2.2

Cancel the common factors.

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Step 1.3.3.1.2.2.1

Factor $- 3$ out of $- 3$ .

$y = - 1 + \frac{- 3 (4 x)}{- 3 (1)}$

Step 1.3.3.1.2.2.2

Cancel the common factor.

$y = - 1 + \frac{- 3 (4 x)}{- 3 \cdot 1}$

Step 1.3.3.1.2.2.3

Rewrite the expression.

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

Step 1.3.3.1.2.2.4

Divide $4 x$ by $1$ .

$y = - 1 + 4 x$

Step 1.4

Reorder $- 1$ and $4 x$ .

$y = 4 x - 1$

Step 2

Using the slope-intercept form, the slope is $4$ .

$m_{1} = 4$

Step 3

Use the slope-intercept form to find the slope.

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Step 3.1

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 3.2

Using the slope-intercept form, the slope is $4$ .

$m_{2} = 4$

Step 4

Since the slopes are the same, the lines are parallel and do not intersect, so the system has no solutions.

$m_{1} = 4$

$m_{2} = 4$

Step 5