Finite Math Examples

$x = 2 y$ ,

$y = - 2 x$

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

Rewrite the equation as

$2 y = x$ .

$2 y = x$

Step 1.3

Divide each term in

$2 y = x$ by

$2$ and simplify.

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Step 1.3.1

Divide each term in

$2 y = x$ by

$2$ .

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

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of

$2$ .

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Step 1.3.2.1.1

Cancel the common factor.

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

Step 1.3.2.1.2

Divide

$y$ by

$1$ .

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

Step 1.4

Reorder terms.

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

Step 2

Using the slope-intercept form, the slope is

$\frac{1}{2}$ .

$m_{1} = \frac{1}{2}$

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

$- 2$ .

$m_{2} = - 2$

Step 4

Set up the system of equations to find any points of intersection.

$x = 2 y, y = - 2 x$

Step 5

Solve the system of equations to find the point of intersection.

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Step 5.1

Replace all occurrences of

$x$ with

$2 y$ in each equation.

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Step 5.1.1

Replace all occurrences of

$x$ in

$y = - 2 x$ with

$2 y$ .

$y = - 2 (2 y)$

$x = 2 y$

Step 5.1.2

Simplify the right side.

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Step 5.1.2.1

Multiply

$2$ by

$- 2$ .

$y = - 4 y$

$x = 2 y$

$y = - 4 y$

$x = 2 y$

$y = - 4 y$

$x = 2 y$

Step 5.2

Solve for

$y$ in

$y = - 4 y$ .

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Step 5.2.1

Move all terms containing

$y$ to the left side of the equation.

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Step 5.2.1.1

Add

$4 y$ to both sides of the equation.

$y + 4 y = 0$

$x = 2 y$

Step 5.2.1.2

Add

$y$ and

$4 y$ .

$5 y = 0$

$x = 2 y$

$5 y = 0$

$x = 2 y$

Step 5.2.2

Divide each term in

$5 y = 0$ by

$5$ and simplify.

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Step 5.2.2.1

Divide each term in

$5 y = 0$ by

$5$ .

$\frac{5 y}{5} = \frac{0}{5}$

$x = 2 y$

Step 5.2.2.2

Simplify the left side.

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Step 5.2.2.2.1

Cancel the common factor of

$5$ .

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Step 5.2.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{0}{5}$

$x = 2 y$

Step 5.2.2.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{0}{5}$

$x = 2 y$

$y = \frac{0}{5}$

$x = 2 y$

$y = \frac{0}{5}$

$x = 2 y$

Step 5.2.2.3

Simplify the right side.

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Step 5.2.2.3.1

Divide

$0$ by

$5$ .

$y = 0$

$x = 2 y$

$y = 0$

$x = 2 y$

$y = 0$

$x = 2 y$

$y = 0$

$x = 2 y$

Step 5.3

Replace all occurrences of

$y$ with

$0$ in each equation.

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Step 5.3.1

Replace all occurrences of

$y$ in

$x = 2 y$ with

$0$ .

$x = 2 (0)$

$y = 0$

Step 5.3.2

Simplify the right side.

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Step 5.3.2.1

Multiply

$2$ by

$0$ .

$x = 0$

$y = 0$

$x = 0$

$y = 0$

$x = 0$

$y = 0$

Step 5.4

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

$(0, 0)$

Step 6

Since the slopes are different, the lines will have exactly one intersection point.

$m_{1} = \frac{1}{2}$

$m_{2} = - 2$

$(0, 0)$

Step 7