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

$2 x + 3 y = 6$

Step 1

Solve the equation for $y$ .

Subtract $2 x$ from both sides of the equation.

$3 y = 6 - 2 x$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $6$ by $3$ .

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

Move the negative in front of the fraction.

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

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.

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

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

Simplify each term.

Cancel the common factor of $0$ and $3$ .

Factor $3$ out of $2 (0)$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

$y = 2 - \frac{3 (2 \cdot (0))}{3 (1)}$

Cancel the common factor.

$y = 2 - \frac{3 (2 \cdot (0))}{3 \cdot 1}$

Rewrite the expression.

$y = 2 - \frac{2 \cdot (0)}{1}$

Divide $2 \cdot (0)$ by $1$ .

$y = 2 - (2 \cdot (0))$

Multiply $- (2 \cdot (0))$ .

Multiply $2$ by $0$ .

$y = 2 - 0$

Multiply $- 1$ by $0$ .

$y = 2 + 0$

Add $2$ and $0$ .

$y = 2$

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

$(0, 2)$

Step 4

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

Remove parentheses.

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

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

Multiply $2$ by $1$ .

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $3$ .

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

Subtract $2$ from $6$ .

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

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

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

Step 5

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

Remove parentheses.

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

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

Multiply $2$ by $2$ .

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $3$ .

$y = \frac{6 - 4}{3}$

Subtract $4$ from $6$ .

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

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

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

Step 6

These are three possible solutions to the equation.

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

Step 7

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

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