Find Three Ordered Pair Solutions 4x-1=3y+5

$4 x - 1 = 3 y + 5$

Step 1

Solve the equation for $y$ .

Rewrite the equation as $3 y + 5 = 4 x - 1$ .

$3 y + 5 = 4 x - 1$

Move all terms not containing $y$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$3 y = 4 x - 1 - 5$

Subtract $5$ from $- 1$ .

$3 y = 4 x - 6$

Divide each term in $3 y = 4 x - 6$ by $3$ and simplify.

Divide each term in $3 y = 4 x - 6$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $- 6$ by $3$ .

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

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.

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

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

Multiply $4$ by $0$ .

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

Divide $0$ by $3$ .

$y = 0 - 2$

Subtract $2$ from $0$ .

$y = - 2$

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.

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

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

Multiply $4$ by $1$ .

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 2$ by $3$ .

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

Subtract $6$ from $4$ .

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

Move the negative in front of the fraction.

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

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

$(1, - \frac{2}{3})$

Step 5

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

Remove parentheses.

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

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

Multiply $4$ by $2$ .

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

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

$y = \frac{8}{3} - 2 \cdot \frac{3}{3}$

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

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

Combine the numerators over the common denominator.

$y = \frac{8 - 2 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 2$ by $3$ .

$y = \frac{8 - 6}{3}$

Subtract $6$ from $8$ .

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

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.

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

Step 7

Find Three Ordered Pair Solutions 4x-1=3y+5

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