Find Three Ordered Pair Solutions 3x-y=6

$3 x - y = 6$

Step 1

Solve the equation for $y$ .

Subtract $3 x$ from both sides of the equation.

$- y = 6 - 3 x$

Divide each term in $- y = 6 - 3 x$ by $- 1$ and simplify.

Divide each term in $- y = 6 - 3 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{6}{- 1} + \frac{- 3 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{6}{- 1} + \frac{- 3 x}{- 1}$

Divide $y$ by $1$ .

$y = \frac{6}{- 1} + \frac{- 3 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 1$ .

$y = - 6 + \frac{- 3 x}{- 1}$

Move the negative one from the denominator of $\frac{- 3 x}{- 1}$ .

$y = - 6 - 1 \cdot (- 3 x)$

Rewrite $- 1 \cdot (- 3 x)$ as $- (- 3 x)$ .

$y = - 6 - (- 3 x)$

Multiply $- 3$ by $- 1$ .

$y = - 6 + 3 x$

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.

$y = - 6 + 3 (0)$

Simplify $- 6 + 3 (0)$ .

Multiply $3$ by $0$ .

$y = - 6 + 0$

Add $- 6$ and $0$ .

$y = - 6$

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

$(0, - 6)$

Step 4

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

Remove parentheses.

$y = - 6 + 3 (1)$

Simplify $- 6 + 3 (1)$ .

Multiply $3$ by $1$ .

$y = - 6 + 3$

Add $- 6$ and $3$ .

$y = - 3$

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

$(1, - 3)$

Step 5

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

Remove parentheses.

$y = - 6 + 3 (2)$

Simplify $- 6 + 3 (2)$ .

Multiply $3$ by $2$ .

$y = - 6 + 6$

Add $- 6$ and $6$ .

$y = 0$

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

$(2, 0)$

Step 6

These are three possible solutions to the equation.

$(0, - 6), (1, - 3), (2, 0)$

Step 7

Find Three Ordered Pair Solutions 3x-y=6

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