Find Three Ordered Pair Solutions -x-4y=-10

$- x - 4 y = - 10$

Step 1

Solve the equation for $y$ .

Add $x$ to both sides of the equation.

$- 4 y = - 10 + x$

Divide each term in $- 4 y = - 10 + x$ by $- 4$ and simplify.

Divide each term in $- 4 y = - 10 + x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 10}{- 4} + \frac{x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 10}{- 4} + \frac{x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{- 10}{- 4} + \frac{x}{- 4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 10$ and $- 4$ .

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

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

Cancel the common factors.

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

$y = \frac{- 2 \cdot 5}{- 2 \cdot 2} + \frac{x}{- 4}$

Cancel the common factor.

$y = \frac{- 2 \cdot 5}{- 2 \cdot 2} + \frac{x}{- 4}$

Rewrite the expression.

$y = \frac{5}{2} + \frac{x}{- 4}$

Move the negative in front of the fraction.

$y = \frac{5}{2} - \frac{x}{4}$

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.

Remove parentheses.

$y = \frac{5}{2} - \frac{0}{4}$

Simplify $\frac{5}{2} - \frac{0}{4}$ .

Simplify each term.

Divide $0$ by $4$ .

$y = \frac{5}{2} - 0$

Multiply $- 1$ by $0$ .

$y = \frac{5}{2} + 0$

Add $\frac{5}{2}$ and $0$ .

$y = \frac{5}{2}$

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

$(0, \frac{5}{2})$

Step 4

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

Remove parentheses.

$y = \frac{5}{2} - \frac{1}{4}$

Simplify $\frac{5}{2} - \frac{1}{4}$ .

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{5}{2} \cdot \frac{2}{2} - \frac{1}{4}$

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

Multiply $\frac{5}{2}$ by $\frac{2}{2}$ .

$y = \frac{5 \cdot 2}{2 \cdot 2} - \frac{1}{4}$

Multiply $2$ by $2$ .

$y = \frac{5 \cdot 2}{4} - \frac{1}{4}$

Combine the numerators over the common denominator.

$y = \frac{5 \cdot 2 - 1}{4}$

Simplify the numerator.

Multiply $5$ by $2$ .

$y = \frac{10 - 1}{4}$

Subtract $1$ from $10$ .

$y = \frac{9}{4}$

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

$(1, \frac{9}{4})$

Step 5

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

Remove parentheses.

$y = \frac{5}{2} - \frac{2}{4}$

Simplify $\frac{5}{2} - \frac{2}{4}$ .

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$y = \frac{5}{2} - \frac{2 (1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = \frac{5}{2} - \frac{2 \cdot 1}{2 \cdot 2}$

Cancel the common factor.

$y = \frac{5}{2} - \frac{2 \cdot 1}{2 \cdot 2}$

Rewrite the expression.

$y = \frac{5}{2} - \frac{1}{2}$

Combine the numerators over the common denominator.

$y = \frac{5 - 1}{2}$

Simplify the expression.

Subtract $1$ from $5$ .

$y = \frac{4}{2}$

Divide $4$ by $2$ .

$y = 2$

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

$(2, 2)$

Step 6

These are three possible solutions to the equation.

$(0, \frac{5}{2}), (1, \frac{9}{4}), (2, 2)$

Step 7

Find Three Ordered Pair Solutions -x-4y=-10

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