Find Three Ordered Pair Solutions -x+4y=9

$- x + 4 y = 9$

Step 1

Solve the equation for $y$ .

Add $x$ to both sides of the equation.

$4 y = 9 + x$

Divide each term in $4 y = 9 + x$ by $4$ and simplify.

Divide each term in $4 y = 9 + x$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

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.

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

Simplify $\frac{9}{4} + \frac{0}{4}$ .

Combine the numerators over the common denominator.

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

Add $9$ and $0$ .

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

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

$(0, \frac{9}{4})$

Step 4

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

Remove parentheses.

$y = \frac{9}{4} + \frac{1}{4}$

Simplify $\frac{9}{4} + \frac{1}{4}$ .

Combine the numerators over the common denominator.

$y = \frac{9 + 1}{4}$

Add $9$ and $1$ .

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

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

Factor $2$ out of $10$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

$(1, \frac{5}{2})$

Step 5

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

Remove parentheses.

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

Simplify $\frac{9}{4} + \frac{2}{4}$ .

Combine the numerators over the common denominator.

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

Add $9$ and $2$ .

$y = \frac{11}{4}$

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

$(2, \frac{11}{4})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{9}{4}), (1, \frac{5}{2}), (2, \frac{11}{4})$

Step 7

Find Three Ordered Pair Solutions -x+4y=9

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