Find Three Ordered Pair Solutions -3x+2y=8

$- 3 x + 2 y = 8$

Step 1

Solve the equation for $y$ .

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

$2 y = 8 + 3 x$

Divide each term in $2 y = 8 + 3 x$ by $2$ and simplify.

Divide each term in $2 y = 8 + 3 x$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $8$ by $2$ .

$y = 4 + \frac{3 x}{2}$

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.

$y = 4 + \frac{3 (0)}{2}$

Simplify $4 + \frac{3 (0)}{2}$ .

Multiply $3$ by $0$ .

$y = 4 + \frac{0}{2}$

Divide $0$ by $2$ .

$y = 4 + 0$

Add $4$ and $0$ .

$y = 4$

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

$(0, 4)$

Step 4

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

Remove parentheses.

$y = 4 + \frac{3 (1)}{2}$

Simplify $4 + \frac{3 (1)}{2}$ .

Multiply $3$ by $1$ .

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

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

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

Combine $4$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $4$ by $2$ .

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

Add $8$ and $3$ .

$y = \frac{11}{2}$

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

$(1, \frac{11}{2})$

Step 5

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

Remove parentheses.

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

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

Multiply $3$ by $2$ .

$y = 4 + \frac{6}{2}$

Divide $6$ by $2$ .

$y = 4 + 3$

Add $4$ and $3$ .

$y = 7$

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

$(2, 7)$

Step 6

These are three possible solutions to the equation.

$(0, 4), (1, \frac{11}{2}), (2, 7)$

Step 7

Find Three Ordered Pair Solutions -3x+2y=8

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