Find Three Ordered Pair Solutions x+y+z=0

$x + y + z = 0$

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

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Subtract $x$ from both sides of the equation.

$y + z = - x$

Subtract $z$ from both sides of the equation.

$y = - x - z$

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

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

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Remove parentheses.

$y = - (0) - (1)$

Simplify $- (0) - (1)$ .

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Simplify each term.

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Multiply $- 1$ by $0$ .

$y = 0 - (1)$

Multiply $- 1$ by $1$ .

$y = 0 - 1$

Subtract $1$ from $0$ .

$y = - 1$

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

$(0, - 1, 1)$

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

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Remove parentheses.

$y = - (1) - (2)$

Simplify $- (1) - (2)$ .

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Simplify each term.

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Multiply $- 1$ by $1$ .

$y = - 1 - (2)$

Multiply $- 1$ by $2$ .

$y = - 1 - 2$

Subtract $2$ from $- 1$ .

$y = - 3$

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

$(1, - 3, 2)$

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

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Remove parentheses.

$y = - (2) - (3)$

Simplify $- (2) - (3)$ .

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Simplify each term.

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Multiply $- 1$ by $2$ .

$y = - 2 - (3)$

Multiply $- 1$ by $3$ .

$y = - 2 - 3$

Subtract $3$ from $- 2$ .

$y = - 5$

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

$(2, - 5, 3)$

These are three possible solutions to the equation.

$(0, - 1, 1), (1, - 3, 2), (2, - 5, 3)$

Find Three Ordered Pair Solutions x+y+z=0

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