Algebra Examples

$- 2 x - 3 y + 5 z = 7$

Step 1

Solve the equation for $y$ .

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Add $2 x$ to both sides of the equation.

$- 3 y + 5 z = 7 + 2 x$

Step 1.1.2

Subtract $5 z$ from both sides of the equation.

$- 3 y = 7 + 2 x - 5 z$

Step 1.2

Divide each term in $- 3 y = 7 + 2 x - 5 z$ by $- 3$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $- 3 y = 7 + 2 x - 5 z$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{7}{- 3} + \frac{2 x}{- 3} + \frac{- 5 z}{- 3}$

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.

$\frac{- 3 y}{- 3} = \frac{7}{- 3} + \frac{2 x}{- 3} + \frac{- 5 z}{- 3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{7}{- 3} + \frac{2 x}{- 3} + \frac{- 5 z}{- 3}$

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.

$y = - \frac{7}{3} + \frac{2 x}{- 3} + \frac{- 5 z}{- 3}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{7}{3} - \frac{2 x}{3} + \frac{- 5 z}{- 3}$

Step 1.2.3.1.3

Dividing two negative values results in a positive value.

$y = - \frac{7}{3} - \frac{2 x}{3} + \frac{5 z}{3}$

Step 2

Choose any values for $x$ and $y$ that are in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ and $1$ to substitute for $z$ .

Tap for more steps...

Step 3.1

Remove parentheses.

$y = - \frac{7}{3} - \frac{2 (0)}{3} + \frac{5 (1)}{3}$

Step 3.2

Simplify $- \frac{7}{3} - \frac{2 (0)}{3} + \frac{5 (1)}{3}$ .

Tap for more steps...

Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{- 7 - 2 \cdot 0 + 5 (1)}{3}$

Step 3.2.2

Simplify each term.

Tap for more steps...

Step 3.2.2.1

Multiply $- 2$ by $0$ .

$y = \frac{- 7 + 0 + 5 (1)}{3}$

Step 3.2.2.2

Multiply $5$ by $1$ .

$y = \frac{- 7 + 0 + 5}{3}$

Step 3.2.3

Simplify the expression.

Tap for more steps...

Step 3.2.3.1

Add $- 7$ and $0$ .

$y = \frac{- 7 + 5}{3}$

Step 3.2.3.2

Add $- 7$ and $5$ .

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

Step 3.2.3.3

Move the negative in front of the fraction.

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

Step 3.3

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

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

Step 4

Choose $1$ to substitute in for $x$ and $2$ to substitute for $z$ .

Tap for more steps...

Step 4.1

Remove parentheses.

$y = - \frac{7}{3} - \frac{2 (1)}{3} + \frac{5 (2)}{3}$

Step 4.2

Simplify $- \frac{7}{3} - \frac{2 (1)}{3} + \frac{5 (2)}{3}$ .

Tap for more steps...

Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{- 7 - 2 \cdot 1 + 5 (2)}{3}$

Step 4.2.2

Simplify each term.

Tap for more steps...

Step 4.2.2.1

Multiply $- 2$ by $1$ .

$y = \frac{- 7 - 2 + 5 (2)}{3}$

Step 4.2.2.2

Multiply $5$ by $2$ .

$y = \frac{- 7 - 2 + 10}{3}$

Step 4.2.3

Simplify by adding and subtracting.

Tap for more steps...

Step 4.2.3.1

Subtract $2$ from $- 7$ .

$y = \frac{- 9 + 10}{3}$

Step 4.2.3.2

Add $- 9$ and $10$ .

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

Step 4.3

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

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

Step 5

Choose $2$ to substitute in for $x$ and $3$ to substitute for $z$ .

Tap for more steps...

Step 5.1

Remove parentheses.

$y = - \frac{7}{3} - \frac{2 (2)}{3} + \frac{5 (3)}{3}$

Step 5.2

Simplify $- \frac{7}{3} - \frac{2 (2)}{3} + \frac{5 (3)}{3}$ .

Tap for more steps...

Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{- 7 - 2 \cdot 2 + 5 (3)}{3}$

Step 5.2.2

Simplify each term.

Tap for more steps...

Step 5.2.2.1

Multiply $- 2$ by $2$ .

$y = \frac{- 7 - 4 + 5 (3)}{3}$

Step 5.2.2.2

Multiply $5$ by $3$ .

$y = \frac{- 7 - 4 + 15}{3}$

Step 5.2.3

Simplify by adding and subtracting.

Tap for more steps...

Step 5.2.3.1

Subtract $4$ from $- 7$ .

$y = \frac{- 11 + 15}{3}$

Step 5.2.3.2

Add $- 11$ and $15$ .

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

Step 5.3

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

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

Step 6

These are three possible solutions to the equation.

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