Find Three Ordered Pair Solutions 12x-8y=12

$12 x - 8 y = 12$

Step 1

Solve the equation for $y$ .

Subtract $12 x$ from both sides of the equation.

$- 8 y = 12 - 12 x$

Divide each term in $- 8 y = 12 - 12 x$ by $- 8$ and simplify.

Divide each term in $- 8 y = 12 - 12 x$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{12}{- 8} + \frac{- 12 x}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{12}{- 8} + \frac{- 12 x}{- 8}$

Divide $y$ by $1$ .

$y = \frac{12}{- 8} + \frac{- 12 x}{- 8}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $12$ and $- 8$ .

Factor $4$ out of $12$ .

$y = \frac{4 (3)}{- 8} + \frac{- 12 x}{- 8}$

Cancel the common factors.

Factor $4$ out of $- 8$ .

$y = \frac{4 \cdot 3}{4 \cdot - 2} + \frac{- 12 x}{- 8}$

Cancel the common factor.

$y = \frac{4 \cdot 3}{4 \cdot - 2} + \frac{- 12 x}{- 8}$

Rewrite the expression.

$y = \frac{3}{- 2} + \frac{- 12 x}{- 8}$

Move the negative in front of the fraction.

$y = - \frac{3}{2} + \frac{- 12 x}{- 8}$

Cancel the common factor of $- 12$ and $- 8$ .

Factor $- 4$ out of $- 12 x$ .

$y = - \frac{3}{2} + \frac{- 4 (3 x)}{- 8}$

Cancel the common factors.

Factor $- 4$ out of $- 8$ .

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

Cancel the common factor.

$y = - \frac{3}{2} + \frac{- 4 (3 x)}{- 4 \cdot 2}$

Rewrite the expression.

$y = - \frac{3}{2} + \frac{3 x}{2}$

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.

Remove parentheses.

$y = - \frac{3}{2} + \frac{3 (0)}{2}$

Simplify $- \frac{3}{2} + \frac{3 (0)}{2}$ .

Combine the numerators over the common denominator.

$y = \frac{- 3 + 3 (0)}{2}$

Simplify the expression.

Multiply $3$ by $0$ .

$y = \frac{- 3 + 0}{2}$

Add $- 3$ and $0$ .

$y = \frac{- 3}{2}$

Move the negative in front of the fraction.

$y = - \frac{3}{2}$

Use the $x$ and $y$ values to form the ordered pair.

$(0, - \frac{3}{2})$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = - \frac{3}{2} + \frac{3 (1)}{2}$

Simplify $- \frac{3}{2} + \frac{3 (1)}{2}$ .

Combine the numerators over the common denominator.

$y = \frac{- 3 + 3 (1)}{2}$

Simplify the expression.

Multiply $3$ by $1$ .

$y = \frac{- 3 + 3}{2}$

Add $- 3$ and $3$ .

$y = \frac{0}{2}$

Divide $0$ by $2$ .

$y = 0$

Use the $x$ and $y$ values to form the ordered pair.

$(1, 0)$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

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

Simplify $- \frac{3}{2} + \frac{3 (2)}{2}$ .

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $3$ by $2$ .

$y = \frac{- 3 + 6}{2}$

Add $- 3$ and $6$ .

$y = \frac{3}{2}$

Use the $x$ and $y$ values to form the ordered pair.

$(2, \frac{3}{2})$

Step 6

These are three possible solutions to the equation.

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

Step 7

Find Three Ordered Pair Solutions 12x-8y=12

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