Finite Math Examples

$2 x - 7 y = 4$

Step 1

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

$2 (- 2) - 7 y = 4$

Step 2

Solve the equation for $y$ .

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Step 2.1

Multiply $2$ by $- 2$ .

$- 4 - 7 y = 4$

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 $4$ to both sides of the equation.

$- 7 y = 4 + 4$

Step 2.2.2

Add $4$ and $4$ .

$- 7 y = 8$

Step 2.3

Divide each term in $- 7 y = 8$ by $- 7$ and simplify.

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Step 2.3.1

Divide each term in $- 7 y = 8$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{8}{- 7}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 7$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{8}{- 7}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{8}{- 7}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Move the negative in front of the fraction.

$y = - \frac{8}{7}$

Step 3

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

$2 (- 1) - 7 y = 4$

Step 4

Solve the equation for $y$ .

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Step 4.1

Multiply $2$ by $- 1$ .

$- 2 - 7 y = 4$

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 $2$ to both sides of the equation.

$- 7 y = 4 + 2$

Step 4.2.2

Add $4$ and $2$ .

$- 7 y = 6$

Step 4.3

Divide each term in $- 7 y = 6$ by $- 7$ and simplify.

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Step 4.3.1

Divide each term in $- 7 y = 6$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{6}{- 7}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 7$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{6}{- 7}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{6}{- 7}$

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.

$y = - \frac{6}{7}$

Step 5

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

$2 (0) - 7 y = 4$

Step 6

Solve the equation for $y$ .

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Step 6.1

Simplify $2 (0) - 7 y$ .

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Step 6.1.1

Multiply $2$ by $0$ .

$0 - 7 y = 4$

Step 6.1.2

Subtract $7 y$ from $0$ .

$- 7 y = 4$

Step 6.2

Divide each term in $- 7 y = 4$ by $- 7$ and simplify.

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Step 6.2.1

Divide each term in $- 7 y = 4$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{4}{- 7}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $- 7$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{4}{- 7}$

Step 6.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{4}{- 7}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Move the negative in front of the fraction.

$y = - \frac{4}{7}$

Step 7

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

$2 (1) - 7 y = 4$

Step 8

Solve the equation for $y$ .

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Step 8.1

Multiply $2$ by $1$ .

$2 - 7 y = 4$

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 $2$ from both sides of the equation.

$- 7 y = 4 - 2$

Step 8.2.2

Subtract $2$ from $4$ .

$- 7 y = 2$

Step 8.3

Divide each term in $- 7 y = 2$ by $- 7$ and simplify.

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Step 8.3.1

Divide each term in $- 7 y = 2$ by $- 7$ .

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

Step 8.3.2

Simplify the left side.

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Step 8.3.2.1

Cancel the common factor of $- 7$ .

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Step 8.3.2.1.1

Cancel the common factor.

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

Step 8.3.2.1.2

Divide $y$ by $1$ .

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

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.

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

Step 9

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

$2 (2) - 7 y = 4$

Step 10

Solve the equation for $y$ .

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Step 10.1

Multiply $2$ by $2$ .

$4 - 7 y = 4$

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 $4$ from both sides of the equation.

$- 7 y = 4 - 4$

Step 10.2.2

Subtract $4$ from $4$ .

$- 7 y = 0$

Step 10.3

Divide each term in $- 7 y = 0$ by $- 7$ and simplify.

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Step 10.3.1

Divide each term in $- 7 y = 0$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{0}{- 7}$

Step 10.3.2

Simplify the left side.

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Step 10.3.2.1

Cancel the common factor of $- 7$ .

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Step 10.3.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{0}{- 7}$

Step 10.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{0}{- 7}$

Step 10.3.3

Simplify the right side.

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Step 10.3.3.1

Divide $0$ by $- 7$ .

$y = 0$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - \frac{8}{7} \\ - 1 & - \frac{6}{7} \\ 0 & - \frac{4}{7} \\ 1 & - \frac{2}{7} \\ 2 & 0 \end{array}$

Step 12