Find Three Ordered Pair Solutions 5x+2y=30

$5 x + 2 y = 30$

Step 1

Solve the equation for $y$ .

Subtract $5 x$ from both sides of the equation.

$2 y = 30 - 5 x$

Divide each term in $2 y = 30 - 5 x$ by $2$ and simplify.

Divide each term in $2 y = 30 - 5 x$ by $2$ .

$\frac{2 y}{2} = \frac{30}{2} + \frac{- 5 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{30}{2} + \frac{- 5 x}{2}$

Divide $y$ by $1$ .

$y = \frac{30}{2} + \frac{- 5 x}{2}$

Simplify the right side.

Simplify each term.

Divide $30$ by $2$ .

$y = 15 + \frac{- 5 x}{2}$

Move the negative in front of the fraction.

$y = 15 - \frac{5 x}{2}$

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.

$y = 15 - \frac{5 (0)}{2}$

Simplify $15 - \frac{5 (0)}{2}$ .

Simplify each term.

Cancel the common factor of $0$ and $2$ .

Factor $2$ out of $5 (0)$ .

$y = 15 - \frac{2 (5 \cdot (0))}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$y = 15 - \frac{2 (5 \cdot (0))}{2 (1)}$

Cancel the common factor.

$y = 15 - \frac{2 (5 \cdot (0))}{2 \cdot 1}$

Rewrite the expression.

$y = 15 - \frac{5 \cdot (0)}{1}$

Divide $5 \cdot (0)$ by $1$ .

$y = 15 - (5 \cdot (0))$

Multiply $- (5 \cdot (0))$ .

Multiply $5$ by $0$ .

$y = 15 - 0$

Multiply $- 1$ by $0$ .

$y = 15 + 0$

Add $15$ and $0$ .

$y = 15$

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

$(0, 15)$

Step 4

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

Remove parentheses.

$y = 15 - \frac{5 (1)}{2}$

Simplify $15 - \frac{5 (1)}{2}$ .

Multiply $5$ by $1$ .

$y = 15 - \frac{5}{2}$

To write $15$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = 15 \cdot \frac{2}{2} - \frac{5}{2}$

Combine $15$ and $\frac{2}{2}$ .

$y = \frac{15 \cdot 2}{2} - \frac{5}{2}$

Combine the numerators over the common denominator.

$y = \frac{15 \cdot 2 - 5}{2}$

Simplify the numerator.

Multiply $15$ by $2$ .

$y = \frac{30 - 5}{2}$

Subtract $5$ from $30$ .

$y = \frac{25}{2}$

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

$(1, \frac{25}{2})$

Step 5

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

Remove parentheses.

$y = 15 - \frac{5 (2)}{2}$

Simplify $15 - \frac{5 (2)}{2}$ .

Simplify each term.

Cancel the common factor of $2$ .

Cancel the common factor.

$y = 15 - \frac{5 \cdot 2}{2}$

Divide $5$ by $1$ .

$y = 15 - 1 \cdot 5$

Multiply $- 1$ by $5$ .

$y = 15 - 5$

Subtract $5$ from $15$ .

$y = 10$

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

$(2, 10)$

Step 6

These are three possible solutions to the equation.

$(0, 15), (1, \frac{25}{2}), (2, 10)$

Step 7

Find Three Ordered Pair Solutions 5x+2y=30

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