Find Three Ordered Pair Solutions 2y-3x=6

$2 y - 3 x = 6$

Step 1

Solve the equation for $y$ .

Add $3 x$ to both sides of the equation.

$2 y = 6 + 3 x$

Divide each term in $2 y = 6 + 3 x$ by $2$ and simplify.

Divide each term in $2 y = 6 + 3 x$ by $2$ .

$\frac{2 y}{2} = \frac{6}{2} + \frac{3 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{6}{2} + \frac{3 x}{2}$

Divide $y$ by $1$ .

$y = \frac{6}{2} + \frac{3 x}{2}$

Simplify the right side.

Divide $6$ by $2$ .

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

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.

$y = 3 + \frac{3 (0)}{2}$

Simplify $3 + \frac{3 (0)}{2}$ .

Multiply $3$ by $0$ .

$y = 3 + \frac{0}{2}$

Divide $0$ by $2$ .

$y = 3 + 0$

Add $3$ and $0$ .

$y = 3$

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

$(0, 3)$

Step 4

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

Remove parentheses.

$y = 3 + \frac{3 (1)}{2}$

Simplify $3 + \frac{3 (1)}{2}$ .

Multiply $3$ by $1$ .

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

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

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

Combine $3$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $2$ .

$y = \frac{6 + 3}{2}$

Add $6$ and $3$ .

$y = \frac{9}{2}$

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

$(1, \frac{9}{2})$

Step 5

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

Remove parentheses.

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

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

Multiply $3$ by $2$ .

$y = 3 + \frac{6}{2}$

Divide $6$ by $2$ .

$y = 3 + 3$

Add $3$ and $3$ .

$y = 6$

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

$(2, 6)$

Step 6

These are three possible solutions to the equation.

$(0, 3), (1, \frac{9}{2}), (2, 6)$

Step 7

Find Three Ordered Pair Solutions 2y-3x=6

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