Find Three Ordered Pair Solutions -5x+4y=16

$- 5 x + 4 y = 16$

Step 1

Solve the equation for $y$ .

Add $5 x$ to both sides of the equation.

$4 y = 16 + 5 x$

Divide each term in $4 y = 16 + 5 x$ by $4$ and simplify.

Divide each term in $4 y = 16 + 5 x$ by $4$ .

$\frac{4 y}{4} = \frac{16}{4} + \frac{5 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{16}{4} + \frac{5 x}{4}$

Divide $y$ by $1$ .

$y = \frac{16}{4} + \frac{5 x}{4}$

Simplify the right side.

Divide $16$ by $4$ .

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

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.

$y = 4 + \frac{5 (0)}{4}$

Simplify $4 + \frac{5 (0)}{4}$ .

Multiply $5$ by $0$ .

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

Divide $0$ by $4$ .

$y = 4 + 0$

Add $4$ and $0$ .

$y = 4$

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

$(0, 4)$

Step 4

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

Remove parentheses.

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

Simplify $4 + \frac{5 (1)}{4}$ .

Multiply $5$ by $1$ .

$y = 4 + \frac{5}{4}$

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = 4 \cdot \frac{4}{4} + \frac{5}{4}$

Combine $4$ and $\frac{4}{4}$ .

$y = \frac{4 \cdot 4}{4} + \frac{5}{4}$

Combine the numerators over the common denominator.

$y = \frac{4 \cdot 4 + 5}{4}$

Simplify the numerator.

Multiply $4$ by $4$ .

$y = \frac{16 + 5}{4}$

Add $16$ and $5$ .

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

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.

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

Simplify $4 + \frac{5 (2)}{4}$ .

Multiply $5$ by $2$ .

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

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

Factor $2$ out of $10$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $4$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $4$ by $2$ .

$y = \frac{8 + 5}{2}$

Add $8$ and $5$ .

$y = \frac{13}{2}$

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

$(2, \frac{13}{2})$

Step 6

These are three possible solutions to the equation.

$(0, 4), (1, \frac{21}{4}), (2, \frac{13}{2})$

Step 7

Find Three Ordered Pair Solutions -5x+4y=16

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