Find Three Ordered Pair Solutions 2x-3y-5=0

$2 x - 3 y - 5 = 0$

Step 1

Solve the equation for $y$ .

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

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

$- 3 y - 5 = - 2 x$

Add $5$ to both sides of the equation.

$- 3 y = - 2 x + 5$

Divide each term in $- 3 y = - 2 x + 5$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 2 x + 5$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 2 x}{- 3} + \frac{5}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 2 x}{- 3} + \frac{5}{- 3}$

Divide $y$ by $1$ .

$y = \frac{- 2 x}{- 3} + \frac{5}{- 3}$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$y = \frac{(2) x}{3} + \frac{5}{- 3}$

Move the negative in front of the fraction.

$y = \frac{2 x}{3} - \frac{5}{3}$

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.

$y = \frac{2 (0)}{3} - \frac{5}{3}$

Simplify $\frac{2 (0)}{3} - \frac{5}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{2 (0) - 5}{3}$

Simplify the expression.

Multiply $2$ by $0$ .

$y = \frac{0 - 5}{3}$

Subtract $5$ from $0$ .

$y = \frac{- 5}{3}$

Move the negative in front of the fraction.

$y = - \frac{5}{3}$

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

$(0, - \frac{5}{3})$

Step 4

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

Remove parentheses.

$y = \frac{2 (1)}{3} - \frac{5}{3}$

Simplify $\frac{2 (1)}{3} - \frac{5}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{2 (1) - 5}{3}$

Simplify the expression.

Multiply $2$ by $1$ .

$y = \frac{2 - 5}{3}$

Subtract $5$ from $2$ .

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

Divide $- 3$ by $3$ .

$y = - 1$

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

$(1, - 1)$

Step 5

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

Remove parentheses.

$y = \frac{2 (2)}{3} - \frac{5}{3}$

Simplify $\frac{2 (2)}{3} - \frac{5}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{2 (2) - 5}{3}$

Simplify the expression.

Multiply $2$ by $2$ .

$y = \frac{4 - 5}{3}$

Subtract $5$ from $4$ .

$y = \frac{- 1}{3}$

Move the negative in front of the fraction.

$y = - \frac{1}{3}$

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

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

Step 6

These are three possible solutions to the equation.

$(0, - \frac{5}{3}), (1, - 1), (2, - \frac{1}{3})$

Step 7

Find Three Ordered Pair Solutions 2x-3y-5=0

Related Questions

Support LCMGCF.com by disabling your adblocker.