Find Three Ordered Pair Solutions 6x-8y=3

$6 x - 8 y = 3$

Step 1

Solve the equation for $y$ .

Subtract $6 x$ from both sides of the equation.

$- 8 y = 3 - 6 x$

Divide each term in $- 8 y = 3 - 6 x$ by $- 8$ and simplify.

Divide each term in $- 8 y = 3 - 6 x$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{3}{- 8} + \frac{- 6 x}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{3}{- 8} + \frac{- 6 x}{- 8}$

Divide $y$ by $1$ .

$y = \frac{3}{- 8} + \frac{- 6 x}{- 8}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{3}{8} + \frac{- 6 x}{- 8}$

Cancel the common factor of $- 6$ and $- 8$ .

Factor $- 2$ out of $- 6 x$ .

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

Cancel the common factors.

Factor $- 2$ out of $- 8$ .

$y = - \frac{3}{8} + \frac{- 2 (3 x)}{- 2 (4)}$

Cancel the common factor.

$y = - \frac{3}{8} + \frac{- 2 (3 x)}{- 2 \cdot 4}$

Rewrite the expression.

$y = - \frac{3}{8} + \frac{3 x}{4}$

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.

$y = - \frac{3}{8} + \frac{3 (0)}{4}$

Simplify $- \frac{3}{8} + \frac{3 (0)}{4}$ .

Multiply $3$ by $0$ .

$y = - \frac{3}{8} + \frac{0}{4}$

Divide $0$ by $4$ .

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

Add $- \frac{3}{8}$ 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.

$y = - \frac{3}{8} + \frac{3 (1)}{4}$

Simplify $- \frac{3}{8} + \frac{3 (1)}{4}$ .

Multiply $3$ by $1$ .

$y = - \frac{3}{8} + \frac{3}{4}$

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{3}{8} + \frac{3}{4} \cdot \frac{2}{2}$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{4}$ by $\frac{2}{2}$ .

$y = - \frac{3}{8} + \frac{3 \cdot 2}{4 \cdot 2}$

Multiply $4$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $2$ .

$y = \frac{- 3 + 6}{8}$

Add $- 3$ and $6$ .

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

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

$(1, \frac{3}{8})$

Step 5

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

Remove parentheses.

$y = - \frac{3}{8} + \frac{3 (2)}{4}$

Simplify $- \frac{3}{8} + \frac{3 (2)}{4}$ .

Multiply $3$ by $2$ .

$y = - \frac{3}{8} + \frac{6}{4}$

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

$y = - \frac{3}{8} + \frac{2 (3)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = - \frac{3}{8} + \frac{3}{2}$

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = - \frac{3}{8} + \frac{3}{2} \cdot \frac{4}{4}$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{2}$ by $\frac{4}{4}$ .

$y = - \frac{3}{8} + \frac{3 \cdot 4}{2 \cdot 4}$

Multiply $2$ by $4$ .

$y = - \frac{3}{8} + \frac{3 \cdot 4}{8}$

Combine the numerators over the common denominator.

$y = \frac{- 3 + 3 \cdot 4}{8}$

Simplify the numerator.

Multiply $3$ by $4$ .

$y = \frac{- 3 + 12}{8}$

Add $- 3$ and $12$ .

$y = \frac{9}{8}$

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

$(2, \frac{9}{8})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{3}{8}), (1, \frac{3}{8}), (2, \frac{9}{8})$

Step 7

Find Three Ordered Pair Solutions 6x-8y=3

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