Finite Math Examples

$(5 x - 4 y) + (- 10 x + 8 y) = (- 3) + (6)$

Step 1

Solve the equation for

$y$ .

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Step 1.1

Simplify

$5 x - 4 y - 10 x + 8 y$ .

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Step 1.1.1

Subtract

$10 x$ from

$5 x$ .

$- 5 x - 4 y + 8 y = - 3 + 6$

Step 1.1.2

Add

$- 4 y$ and

$8 y$ .

$- 5 x + 4 y = - 3 + 6$

Step 1.2

Add

$- 3$ and

$6$ .

$- 5 x + 4 y = 3$

Step 1.3

Add

$5 x$ to both sides of the equation.

$4 y = 3 + 5 x$

Step 1.4

Divide each term in

$4 y = 3 + 5 x$ by

$4$ and simplify.

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Step 1.4.1

Divide each term in

$4 y = 3 + 5 x$ by

$4$ .

$\frac{4 y}{4} = \frac{3}{4} + \frac{5 x}{4}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of

$4$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{3}{4} + \frac{5 x}{4}$

Step 1.4.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{3}{4} + \frac{5 x}{4}$

Step 2

Choose any value for

$x$ that is in the domain to plug into the equation.

Step 3

Choose

$0$ to substitute in for

$x$ to find the ordered pair.

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Step 3.1

Remove parentheses.

$y = \frac{3}{4} + \frac{5 (0)}{4}$

Step 3.2

Simplify

$\frac{3}{4} + \frac{5 (0)}{4}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{3 + 5 (0)}{4}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Multiply

$5$ by

$0$ .

$y = \frac{3 + 0}{4}$

Step 3.2.2.2

Add

$3$ and

$0$ .

$y = \frac{3}{4}$

Step 3.3

Use the

$x$ and

$y$ values to form the ordered pair.

$(0, \frac{3}{4})$

Step 4

Choose

$1$ to substitute in for

$x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = \frac{3}{4} + \frac{5 (1)}{4}$

Step 4.2

Simplify

$\frac{3}{4} + \frac{5 (1)}{4}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{3 + 5 (1)}{4}$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Multiply

$5$ by

$1$ .

$y = \frac{3 + 5}{4}$

Step 4.2.2.2

Add

$3$ and

$5$ .

$y = \frac{8}{4}$

Step 4.2.2.3

Divide

$8$ by

$4$ .

$y = 2$

Step 4.3

Use the

$x$ and

$y$ values to form the ordered pair.

$(1, 2)$

Step 5

Choose

$2$ to substitute in for

$x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

$y = \frac{3}{4} + \frac{5 (2)}{4}$

Step 5.2

Simplify

$\frac{3}{4} + \frac{5 (2)}{4}$ .

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Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{3 + 5 (2)}{4}$

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Multiply

$5$ by

$2$ .

$y = \frac{3 + 10}{4}$

Step 5.2.2.2

Add

$3$ and

$10$ .

$y = \frac{13}{4}$

Step 5.3

Use the

$x$ and

$y$ values to form the ordered pair.

$(2, \frac{13}{4})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{3}{4}), (1, 2), (2, \frac{13}{4})$

Step 7