Finite Math Examples

$3 x - 10 y = 20$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$3 (- 2) - 10 y = 20$

Step 2

Solve the equation for $y$ .

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Step 2.1

Multiply $3$ by $- 2$ .

$- 6 - 10 y = 20$

Step 2.2

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

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Step 2.2.1

Add $6$ to both sides of the equation.

$- 10 y = 20 + 6$

Step 2.2.2

Add $20$ and $6$ .

$- 10 y = 26$

Step 2.3

Divide each term in $- 10 y = 26$ by $- 10$ and simplify.

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Step 2.3.1

Divide each term in $- 10 y = 26$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{26}{- 10}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 10$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{26}{- 10}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{26}{- 10}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Cancel the common factor of $26$ and $- 10$ .

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Step 2.3.3.1.1

Factor $2$ out of $26$ .

$y = \frac{2 (13)}{- 10}$

Step 2.3.3.1.2

Cancel the common factors.

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Step 2.3.3.1.2.1

Factor $2$ out of $- 10$ .

$y = \frac{2 \cdot 13}{2 \cdot - 5}$

Step 2.3.3.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 13}{2 \cdot - 5}$

Step 2.3.3.1.2.3

Rewrite the expression.

$y = \frac{13}{- 5}$

Step 2.3.3.2

Move the negative in front of the fraction.

$y = - \frac{13}{5}$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$3 (- 1) - 10 y = 20$

Step 4

Solve the equation for $y$ .

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Step 4.1

Multiply $3$ by $- 1$ .

$- 3 - 10 y = 20$

Step 4.2

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

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Step 4.2.1

Add $3$ to both sides of the equation.

$- 10 y = 20 + 3$

Step 4.2.2

Add $20$ and $3$ .

$- 10 y = 23$

Step 4.3

Divide each term in $- 10 y = 23$ by $- 10$ and simplify.

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Step 4.3.1

Divide each term in $- 10 y = 23$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{23}{- 10}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 10$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{23}{- 10}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{23}{- 10}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Move the negative in front of the fraction.

$y = - \frac{23}{10}$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$3 (0) - 10 y = 20$

Step 6

Solve the equation for $y$ .

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Step 6.1

Simplify $3 (0) - 10 y$ .

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Step 6.1.1

Multiply $3$ by $0$ .

$0 - 10 y = 20$

Step 6.1.2

Subtract $10 y$ from $0$ .

$- 10 y = 20$

Step 6.2

Divide each term in $- 10 y = 20$ by $- 10$ and simplify.

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Step 6.2.1

Divide each term in $- 10 y = 20$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{20}{- 10}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $- 10$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{20}{- 10}$

Step 6.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{20}{- 10}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Divide $20$ by $- 10$ .

$y = - 2$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$3 (1) - 10 y = 20$

Step 8

Solve the equation for $y$ .

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Step 8.1

Multiply $3$ by $1$ .

$3 - 10 y = 20$

Step 8.2

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

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Step 8.2.1

Subtract $3$ from both sides of the equation.

$- 10 y = 20 - 3$

Step 8.2.2

Subtract $3$ from $20$ .

$- 10 y = 17$

Step 8.3

Divide each term in $- 10 y = 17$ by $- 10$ and simplify.

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Step 8.3.1

Divide each term in $- 10 y = 17$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{17}{- 10}$

Step 8.3.2

Simplify the left side.

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Step 8.3.2.1

Cancel the common factor of $- 10$ .

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Step 8.3.2.1.1

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{17}{- 10}$

Step 8.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{17}{- 10}$

Step 8.3.3

Simplify the right side.

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Step 8.3.3.1

Move the negative in front of the fraction.

$y = - \frac{17}{10}$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$3 (2) - 10 y = 20$

Step 10

Solve the equation for $y$ .

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Step 10.1

Multiply $3$ by $2$ .

$6 - 10 y = 20$

Step 10.2

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

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Step 10.2.1

Subtract $6$ from both sides of the equation.

$- 10 y = 20 - 6$

Step 10.2.2

Subtract $6$ from $20$ .

$- 10 y = 14$

Step 10.3

Divide each term in $- 10 y = 14$ by $- 10$ and simplify.

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Step 10.3.1

Divide each term in $- 10 y = 14$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{14}{- 10}$

Step 10.3.2

Simplify the left side.

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Step 10.3.2.1

Cancel the common factor of $- 10$ .

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Step 10.3.2.1.1

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{14}{- 10}$

Step 10.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{14}{- 10}$

Step 10.3.3

Simplify the right side.

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Step 10.3.3.1

Cancel the common factor of $14$ and $- 10$ .

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Step 10.3.3.1.1

Factor $2$ out of $14$ .

$y = \frac{2 (7)}{- 10}$

Step 10.3.3.1.2

Cancel the common factors.

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Step 10.3.3.1.2.1

Factor $2$ out of $- 10$ .

$y = \frac{2 \cdot 7}{2 \cdot - 5}$

Step 10.3.3.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 7}{2 \cdot - 5}$

Step 10.3.3.1.2.3

Rewrite the expression.

$y = \frac{7}{- 5}$

Step 10.3.3.2

Move the negative in front of the fraction.

$y = - \frac{7}{5}$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & - \frac{13}{5} \\ - 1 & - \frac{23}{10} \\ 0 & - 2 \\ 1 & - \frac{17}{10} \\ 2 & - \frac{7}{5} \end{array}$

Step 12