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