Find Three Ordered Pair Solutions 5x+8y=3

$5 x + 8 y = 3$

Step 1

Solve the equation for $y$ .

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

$8 y = 3 - 5 x$

Divide each term in $8 y = 3 - 5 x$ by $8$ and simplify.

Divide each term in $8 y = 3 - 5 x$ by $8$ .

$\frac{8 y}{8} = \frac{3}{8} + \frac{- 5 x}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{3}{8} + \frac{- 5 x}{8}$

Divide $y$ by $1$ .

$y = \frac{3}{8} + \frac{- 5 x}{8}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{3}{8} - \frac{5 x}{8}$

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.

$y = \frac{3}{8} - \frac{5 (0)}{8}$

Simplify $\frac{3}{8} - \frac{5 (0)}{8}$ .

Combine the numerators over the common denominator.

$y = \frac{3 - 5 \cdot 0}{8}$

Simplify the expression.

Multiply $- 5$ by $0$ .

$y = \frac{3 + 0}{8}$

Add $3$ and $0$ .

$y = \frac{3}{8}$

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

$(0, \frac{3}{8})$

Step 4

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

Remove parentheses.

$y = \frac{3}{8} - \frac{5 (1)}{8}$

Simplify $\frac{3}{8} - \frac{5 (1)}{8}$ .

Combine the numerators over the common denominator.

$y = \frac{3 - 5 \cdot 1}{8}$

Simplify the expression.

Multiply $- 5$ by $1$ .

$y = \frac{3 - 5}{8}$

Subtract $5$ from $3$ .

$y = \frac{- 2}{8}$

Cancel the common factor of $- 2$ and $8$ .

Factor $2$ out of $- 2$ .

$y = \frac{2 (- 1)}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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

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

Step 5

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

Remove parentheses.

$y = \frac{3}{8} - \frac{5 (2)}{8}$

Simplify $\frac{3}{8} - \frac{5 (2)}{8}$ .

Combine the numerators over the common denominator.

$y = \frac{3 - 5 \cdot 2}{8}$

Simplify the expression.

Multiply $- 5$ by $2$ .

$y = \frac{3 - 10}{8}$

Subtract $10$ from $3$ .

$y = \frac{- 7}{8}$

Move the negative in front of the fraction.

$y = - \frac{7}{8}$

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

$(2, - \frac{7}{8})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{3}{8}), (1, - \frac{1}{4}), (2, - \frac{7}{8})$

Step 7

Find Three Ordered Pair Solutions 5x+8y=3

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