Find Three Ordered Pair Solutions 6x-5y=0

$6 x - 5 y = 0$

Step 1

Solve the equation for $y$ .

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

$- 5 y = - 6 x$

Divide each term in $- 5 y = - 6 x$ by $- 5$ and simplify.

Divide each term in $- 5 y = - 6 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{- 6 x}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{- 6 x}{- 5}$

Divide $y$ by $1$ .

$y = \frac{- 6 x}{- 5}$

Simplify the right side.

Dividing two negative values results in a positive value.

$y = \frac{6 x}{5}$

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.

$y = \frac{6 (0)}{5}$

Simplify $\frac{6 (0)}{5}$ .

Cancel the common factor of $0$ and $5$ .

Factor $5$ out of $6 (0)$ .

$y = \frac{5 (6 \cdot (0))}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$y = \frac{5 (6 \cdot (0))}{5 (1)}$

Cancel the common factor.

$y = \frac{5 (6 \cdot (0))}{5 \cdot 1}$

Rewrite the expression.

$y = \frac{6 \cdot (0)}{1}$

Divide $6 \cdot (0)$ by $1$ .

$y = 6 \cdot (0)$

Multiply $6$ 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.

$y = \frac{6 (1)}{5}$

Multiply $6$ by $1$ .

$y = \frac{6}{5}$

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

$(1, \frac{6}{5})$

Step 5

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

Remove parentheses.

$y = \frac{6 (2)}{5}$

Multiply $6$ by $2$ .

$y = \frac{12}{5}$

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

$(2, \frac{12}{5})$

Step 6

These are three possible solutions to the equation.

$(0, 0), (1, \frac{6}{5}), (2, \frac{12}{5})$

Step 7

Find Three Ordered Pair Solutions 6x-5y=0

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