Find Three Ordered Pair Solutions 2x+3y+2z=26

$2 x + 3 y + 2 z = 26$

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.

$3 y + 2 z = 26 - 2 x$

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

$3 y = 26 - 2 x - 2 z$

Divide each term in $3 y = 26 - 2 x - 2 z$ by $3$ and simplify.

Divide each term in $3 y = 26 - 2 x - 2 z$ by $3$ .

$\frac{3 y}{3} = \frac{26}{3} + \frac{- 2 x}{3} + \frac{- 2 z}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{26}{3} + \frac{- 2 x}{3} + \frac{- 2 z}{3}$

Divide $y$ by $1$ .

$y = \frac{26}{3} + \frac{- 2 x}{3} + \frac{- 2 z}{3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = \frac{26}{3} - \frac{(2) x}{3} + \frac{- 2 z}{3}$

Move the negative in front of the fraction.

$y = \frac{26}{3} - \frac{2 x}{3} - \frac{2 z}{3}$

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 $z$ .

Remove parentheses.

$y = \frac{26}{3} - \frac{2 (0)}{3} - \frac{2 (1)}{3}$

Simplify $\frac{26}{3} - \frac{2 (0)}{3} - \frac{2 (1)}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{26 - 2 \cdot 0 - 2 \cdot 1}{3}$

Simplify each term.

Multiply $- 2$ by $0$ .

$y = \frac{26 + 0 - 2 \cdot 1}{3}$

Multiply $- 2$ by $1$ .

$y = \frac{26 + 0 - 2}{3}$

Simplify the expression.

Add $26$ and $0$ .

$y = \frac{26 - 2}{3}$

Subtract $2$ from $26$ .

$y = \frac{24}{3}$

Divide $24$ by $3$ .

$y = 8$

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

$(0, 8, 1)$

Step 4

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

Remove parentheses.

$y = \frac{26}{3} - \frac{2 (1)}{3} - \frac{2 (2)}{3}$

Simplify $\frac{26}{3} - \frac{2 (1)}{3} - \frac{2 (2)}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{26 - 2 \cdot 1 - 2 \cdot 2}{3}$

Simplify each term.

Multiply $- 2$ by $1$ .

$y = \frac{26 - 2 - 2 \cdot 2}{3}$

Multiply $- 2$ by $2$ .

$y = \frac{26 - 2 - 4}{3}$

Simplify by subtracting numbers.

Subtract $2$ from $26$ .

$y = \frac{24 - 4}{3}$

Subtract $4$ from $24$ .

$y = \frac{20}{3}$

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

$(1, \frac{20}{3}, 2)$

Step 5

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

Remove parentheses.

$y = \frac{26}{3} - \frac{2 (2)}{3} - \frac{2 (3)}{3}$

Simplify $\frac{26}{3} - \frac{2 (2)}{3} - \frac{2 (3)}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{26 - 2 \cdot 2 - 2 \cdot 3}{3}$

Simplify each term.

Multiply $- 2$ by $2$ .

$y = \frac{26 - 4 - 2 \cdot 3}{3}$

Multiply $- 2$ by $3$ .

$y = \frac{26 - 4 - 6}{3}$

Simplify by subtracting numbers.

Subtract $4$ from $26$ .

$y = \frac{22 - 6}{3}$

Subtract $6$ from $22$ .

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

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

$(2, \frac{16}{3}, 3)$

Step 6

These are three possible solutions to the equation.

$(0, 8, 1), (1, \frac{20}{3}, 2), (2, \frac{16}{3}, 3)$

Find Three Ordered Pair Solutions 2x+3y+2z=26

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