Find Three Ordered Pair Solutions 6x-8y=0

$6 x - 8 y = 0$

Step 1

Solve the equation for $y$ .

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

$- 8 y = - 6 x$

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

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

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

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$y = \frac{3 x}{4}$

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.

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

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

Cancel the common factor of $0$ and $4$ .

Factor $4$ out of $3 (0)$ .

$y = \frac{4 (3 \cdot (0))}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$y = \frac{4 (3 \cdot (0))}{4 (1)}$

Cancel the common factor.

$y = \frac{4 (3 \cdot (0))}{4 \cdot 1}$

Rewrite the expression.

$y = \frac{3 \cdot (0)}{1}$

Divide $3 \cdot (0)$ by $1$ .

$y = 3 \cdot (0)$

Multiply $3$ by $0$ .

$y = 0$

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

$(0, 0)$

Step 4

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

Remove parentheses.

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

Multiply $3$ by $1$ .

$y = \frac{3}{4}$

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

$(1, \frac{3}{4})$

Step 5

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

Remove parentheses.

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

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $3 (2)$ .

$y = \frac{2 \cdot 3}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = \frac{2 \cdot 3}{2 \cdot 2}$

Cancel the common factor.

$y = \frac{2 \cdot 3}{2 \cdot 2}$

Rewrite the expression.

$y = \frac{3}{2}$

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

$(2, \frac{3}{2})$

Step 6

These are three possible solutions to the equation.

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

Step 7

Find Three Ordered Pair Solutions 6x-8y=0

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