Finite Math Examples

$- x - 5 y + 2 = 90 + 54 x + 6 y$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$- x - 5 \cdot 0 + 2 = 90 + 54 x + 6 (0)$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $- x - 5 \cdot 0 + 2$ .

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Step 1.2.1.1

Multiply $- 5$ by $0$ .

$- x + 0 + 2 = 90 + 54 x + 6 (0)$

Step 1.2.1.2

Add $- x$ and $0$ .

$- x + 2 = 90 + 54 x + 6 (0)$

Step 1.2.2

Simplify $90 + 54 x + 6 (0)$ .

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Step 1.2.2.1

Multiply $6$ by $0$ .

$- x + 2 = 90 + 54 x + 0$

Step 1.2.2.2

Add $90 + 54 x$ and $0$ .

$- x + 2 = 90 + 54 x$

Step 1.2.3

Move all terms containing $x$ to the left side of the equation.

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Step 1.2.3.1

Subtract $54 x$ from both sides of the equation.

$- x + 2 - 54 x = 90$

Step 1.2.3.2

Subtract $54 x$ from $- x$ .

$- 55 x + 2 = 90$

Step 1.2.4

Move all terms not containing $x$ to the right side of the equation.

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Step 1.2.4.1

Subtract $2$ from both sides of the equation.

$- 55 x = 90 - 2$

Step 1.2.4.2

Subtract $2$ from $90$ .

$- 55 x = 88$

Step 1.2.5

Divide each term in $- 55 x = 88$ by $- 55$ and simplify.

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Step 1.2.5.1

Divide each term in $- 55 x = 88$ by $- 55$ .

$\frac{- 55 x}{- 55} = \frac{88}{- 55}$

Step 1.2.5.2

Simplify the left side.

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Step 1.2.5.2.1

Cancel the common factor of $- 55$ .

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Step 1.2.5.2.1.1

Cancel the common factor.

$\frac{- 55 x}{- 55} = \frac{88}{- 55}$

Step 1.2.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{88}{- 55}$

Step 1.2.5.3

Simplify the right side.

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Step 1.2.5.3.1

Cancel the common factor of $88$ and $- 55$ .

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Step 1.2.5.3.1.1

Factor $11$ out of $88$ .

$x = \frac{11 (8)}{- 55}$

Step 1.2.5.3.1.2

Cancel the common factors.

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Step 1.2.5.3.1.2.1

Factor $11$ out of $- 55$ .

$x = \frac{11 \cdot 8}{11 \cdot - 5}$

Step 1.2.5.3.1.2.2

Cancel the common factor.

$x = \frac{11 \cdot 8}{11 \cdot - 5}$

Step 1.2.5.3.1.2.3

Rewrite the expression.

$x = \frac{8}{- 5}$

Step 1.2.5.3.2

Move the negative in front of the fraction.

$x = - \frac{8}{5}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{8}{5}, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$- (0) - 5 y + 2 = 90 + 54 (0) + 6 y$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $- (0) - 5 y + 2$ .

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Step 2.2.1.1

Multiply $- 1$ by $0$ .

$0 - 5 y + 2 = 90 + 54 (0) + 6 y$

Step 2.2.1.2

Subtract $5 y$ from $0$ .

$- 5 y + 2 = 90 + 54 (0) + 6 y$

Step 2.2.2

Simplify $90 + 54 (0) + 6 y$ .

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Step 2.2.2.1

Multiply $54$ by $0$ .

$- 5 y + 2 = 90 + 0 + 6 y$

Step 2.2.2.2

Add $90$ and $0$ .

$- 5 y + 2 = 90 + 6 y$

Step 2.2.3

Move all terms containing $y$ to the left side of the equation.

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Step 2.2.3.1

Subtract $6 y$ from both sides of the equation.

$- 5 y + 2 - 6 y = 90$

Step 2.2.3.2

Subtract $6 y$ from $- 5 y$ .

$- 11 y + 2 = 90$

Step 2.2.4

Move all terms not containing $y$ to the right side of the equation.

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Step 2.2.4.1

Subtract $2$ from both sides of the equation.

$- 11 y = 90 - 2$

Step 2.2.4.2

Subtract $2$ from $90$ .

$- 11 y = 88$

Step 2.2.5

Divide each term in $- 11 y = 88$ by $- 11$ and simplify.

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Step 2.2.5.1

Divide each term in $- 11 y = 88$ by $- 11$ .

$\frac{- 11 y}{- 11} = \frac{88}{- 11}$

Step 2.2.5.2

Simplify the left side.

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Step 2.2.5.2.1

Cancel the common factor of $- 11$ .

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Step 2.2.5.2.1.1

Cancel the common factor.

$\frac{- 11 y}{- 11} = \frac{88}{- 11}$

Step 2.2.5.2.1.2

Divide $y$ by $1$ .

$y = \frac{88}{- 11}$

Step 2.2.5.3

Simplify the right side.

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Step 2.2.5.3.1

Divide $88$ by $- 11$ .

$y = - 8$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 8)$

Step 3

List the intersections.

x-intercept(s): $(- \frac{8}{5}, 0)$

y-intercept(s): $(0, - 8)$

Step 4