Pre-Algebra Examples

$2 x + 3 y = - 14$

Step 1

Solve the equation for $y$ .

Tap for more steps...

Step 1.1

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

$3 y = - 14 - 2 x$

Step 1.2

Divide each term in $3 y = - 14 - 2 x$ by $3$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $3 y = - 14 - 2 x$ by $3$ .

$\frac{3 y}{3} = \frac{- 14}{3} + \frac{- 2 x}{3}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 14}{3} + \frac{- 2 x}{3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 14}{3} + \frac{- 2 x}{3}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.2.3.1.1

Move the negative in front of the fraction.

$y = - \frac{14}{3} + \frac{- 2 x}{3}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{14}{3} - \frac{2 x}{3}$

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.

Tap for more steps...

Step 3.1

Remove parentheses.

$y = - \frac{14}{3} - \frac{2 (0)}{3}$

Step 3.2

Simplify $- \frac{14}{3} - \frac{2 (0)}{3}$ .

Tap for more steps...

Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{- 14 - 2 \cdot 0}{3}$

Step 3.2.2

Simplify the expression.

Tap for more steps...

Step 3.2.2.1

Multiply $- 2$ by $0$ .

$y = \frac{- 14 + 0}{3}$

Step 3.2.2.2

Add $- 14$ and $0$ .

$y = \frac{- 14}{3}$

Step 3.2.2.3

Move the negative in front of the fraction.

$y = - \frac{14}{3}$

Step 3.3

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

$(0, - \frac{14}{3})$

Step 4

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

Tap for more steps...

Step 4.1

Remove parentheses.

$y = - \frac{14}{3} - \frac{2 (1)}{3}$

Step 4.2

Simplify $- \frac{14}{3} - \frac{2 (1)}{3}$ .

Tap for more steps...

Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{- 14 - 2 \cdot 1}{3}$

Step 4.2.2

Simplify the expression.

Tap for more steps...

Step 4.2.2.1

Multiply $- 2$ by $1$ .

$y = \frac{- 14 - 2}{3}$

Step 4.2.2.2

Subtract $2$ from $- 14$ .

$y = \frac{- 16}{3}$

Step 4.2.2.3

Move the negative in front of the fraction.

$y = - \frac{16}{3}$

Step 4.3

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

$(1, - \frac{16}{3})$

Step 5

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

Tap for more steps...

Step 5.1

Remove parentheses.

$y = - \frac{14}{3} - \frac{2 (2)}{3}$

Step 5.2

Simplify $- \frac{14}{3} - \frac{2 (2)}{3}$ .

Tap for more steps...

Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{- 14 - 2 \cdot 2}{3}$

Step 5.2.2

Simplify the expression.

Tap for more steps...

Step 5.2.2.1

Multiply $- 2$ by $2$ .

$y = \frac{- 14 - 4}{3}$

Step 5.2.2.2

Subtract $4$ from $- 14$ .

$y = \frac{- 18}{3}$

Step 5.2.2.3

Divide $- 18$ by $3$ .

$y = - 6$

Step 5.3

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

$(2, - 6)$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{14}{3}), (1, - \frac{16}{3}), (2, - 6)$

Step 7