Find Three Ordered Pair Solutions -4y=-3x-18

$- 4 y = - 3 x - 18$

Step 1

Divide each term in $- 4 y = - 3 x - 18$ by $- 4$ and simplify.

Divide each term in $- 4 y = - 3 x - 18$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 3 x}{- 4} + \frac{- 18}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 3 x}{- 4} + \frac{- 18}{- 4}$

Divide $y$ by $1$ .

$y = \frac{- 3 x}{- 4} + \frac{- 18}{- 4}$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$y = \frac{(3) x}{4} + \frac{- 18}{- 4}$

Cancel the common factor of $- 18$ and $- 4$ .

Factor $- 2$ out of $- 18$ .

$y = \frac{3 x}{4} + \frac{- 2 (9)}{- 4}$

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

$y = \frac{3 x}{4} + \frac{- 2 \cdot 9}{- 2 \cdot 2}$

Cancel the common factor.

$y = \frac{3 x}{4} + \frac{- 2 \cdot 9}{- 2 \cdot 2}$

Rewrite the expression.

$y = \frac{3 x}{4} + \frac{9}{2}$

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.

$y = \frac{3 (0)}{4} + \frac{9}{2}$

Simplify $\frac{3 (0)}{4} + \frac{9}{2}$ .

Multiply $3$ by $0$ .

$y = \frac{0}{4} + \frac{9}{2}$

Divide $0$ by $4$ .

$y = 0 + \frac{9}{2}$

Add $0$ and $\frac{9}{2}$ .

$y = \frac{9}{2}$

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

$(0, \frac{9}{2})$

Step 4

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

Remove parentheses.

$y = \frac{3 (1)}{4} + \frac{9}{2}$

Simplify $\frac{3 (1)}{4} + \frac{9}{2}$ .

Multiply $3$ by $1$ .

$y = \frac{3}{4} + \frac{9}{2}$

To write $\frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{3}{4} + \frac{9}{2} \cdot \frac{2}{2}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{9}{2}$ by $\frac{2}{2}$ .

$y = \frac{3}{4} + \frac{9 \cdot 2}{2 \cdot 2}$

Multiply $2$ by $2$ .

$y = \frac{3}{4} + \frac{9 \cdot 2}{4}$

Combine the numerators over the common denominator.

$y = \frac{3 + 9 \cdot 2}{4}$

Simplify the numerator.

Multiply $9$ by $2$ .

$y = \frac{3 + 18}{4}$

Add $3$ and $18$ .

$y = \frac{21}{4}$

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

$(1, \frac{21}{4})$

Step 5

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

Remove parentheses.

$y = \frac{3 (2)}{4} + \frac{9}{2}$

Simplify $\frac{3 (2)}{4} + \frac{9}{2}$ .

Multiply $3$ by $2$ .

$y = \frac{6}{4} + \frac{9}{2}$

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

$y = \frac{2 (3)}{4} + \frac{9}{2}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = \frac{2 \cdot 3}{2 \cdot 2} + \frac{9}{2}$

Cancel the common factor.

$y = \frac{2 \cdot 3}{2 \cdot 2} + \frac{9}{2}$

Rewrite the expression.

$y = \frac{3}{2} + \frac{9}{2}$

Combine the numerators over the common denominator.

$y = \frac{3 + 9}{2}$

Simplify the expression.

Add $3$ and $9$ .

$y = \frac{12}{2}$

Divide $12$ by $2$ .

$y = 6$

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

$(2, 6)$

Step 6

These are three possible solutions to the equation.

$(0, \frac{9}{2}), (1, \frac{21}{4}), (2, 6)$

Step 7

Find Three Ordered Pair Solutions -4y=-3x-18

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