Find Three Ordered Pair Solutions 12x-10y=18

$12 x - 10 y = 18$

Step 1

Solve the equation for $y$ .

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

$- 10 y = 18 - 12 x$

Divide each term in $- 10 y = 18 - 12 x$ by $- 10$ and simplify.

Divide each term in $- 10 y = 18 - 12 x$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{18}{- 10} + \frac{- 12 x}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{18}{- 10} + \frac{- 12 x}{- 10}$

Divide $y$ by $1$ .

$y = \frac{18}{- 10} + \frac{- 12 x}{- 10}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $18$ and $- 10$ .

Factor $2$ out of $18$ .

$y = \frac{2 (9)}{- 10} + \frac{- 12 x}{- 10}$

Cancel the common factors.

Factor $2$ out of $- 10$ .

$y = \frac{2 \cdot 9}{2 \cdot - 5} + \frac{- 12 x}{- 10}$

Cancel the common factor.

$y = \frac{2 \cdot 9}{2 \cdot - 5} + \frac{- 12 x}{- 10}$

Rewrite the expression.

$y = \frac{9}{- 5} + \frac{- 12 x}{- 10}$

Move the negative in front of the fraction.

$y = - \frac{9}{5} + \frac{- 12 x}{- 10}$

Cancel the common factor of $- 12$ and $- 10$ .

Factor $- 2$ out of $- 12 x$ .

$y = - \frac{9}{5} + \frac{- 2 (6 x)}{- 10}$

Cancel the common factors.

Factor $- 2$ out of $- 10$ .

$y = - \frac{9}{5} + \frac{- 2 (6 x)}{- 2 (5)}$

Cancel the common factor.

$y = - \frac{9}{5} + \frac{- 2 (6 x)}{- 2 \cdot 5}$

Rewrite the expression.

$y = - \frac{9}{5} + \frac{6 x}{5}$

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.

$y = - \frac{9}{5} + \frac{6 (0)}{5}$

Simplify $- \frac{9}{5} + \frac{6 (0)}{5}$ .

Combine the numerators over the common denominator.

$y = \frac{- 9 + 6 (0)}{5}$

Simplify the expression.

Multiply $6$ by $0$ .

$y = \frac{- 9 + 0}{5}$

Add $- 9$ and $0$ .

$y = \frac{- 9}{5}$

Move the negative in front of the fraction.

$y = - \frac{9}{5}$

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

$(0, - \frac{9}{5})$

Step 4

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

Remove parentheses.

$y = - \frac{9}{5} + \frac{6 (1)}{5}$

Simplify $- \frac{9}{5} + \frac{6 (1)}{5}$ .

Combine the numerators over the common denominator.

$y = \frac{- 9 + 6 (1)}{5}$

Simplify the expression.

Multiply $6$ by $1$ .

$y = \frac{- 9 + 6}{5}$

Add $- 9$ and $6$ .

$y = \frac{- 3}{5}$

Move the negative in front of the fraction.

$y = - \frac{3}{5}$

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

$(1, - \frac{3}{5})$

Step 5

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

Remove parentheses.

$y = - \frac{9}{5} + \frac{6 (2)}{5}$

Simplify $- \frac{9}{5} + \frac{6 (2)}{5}$ .

Combine the numerators over the common denominator.

$y = \frac{- 9 + 6 (2)}{5}$

Simplify the expression.

Multiply $6$ by $2$ .

$y = \frac{- 9 + 12}{5}$

Add $- 9$ and $12$ .

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

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

$(2, \frac{3}{5})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{9}{5}), (1, - \frac{3}{5}), (2, \frac{3}{5})$

Step 7

Find Three Ordered Pair Solutions 12x-10y=18

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