Algebra Examples

$x - 4 y + 5 z = 0$ , $x + z - 3 y = 0$

Step 1

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

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Add $4 y$ to both sides of the equation.

$x + 5 z = 4 y$

$x + z - 3 y = 0$

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

$x = 4 y - 5 z$

$x + z - 3 y = 0$

$x = 4 y - 5 z$

$x + z - 3 y = 0$

Step 2

Solve the equation for $z$ .

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Simplify $(4 y - 5 z) + z - 3 y$ .

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Subtract $3 y$ from $4 y$ .

$y - 5 z + z = 0$

$x = 4 y - 5 z$

Add $- 5 z$ and $z$ .

$y - 4 z = 0$

$x = 4 y - 5 z$

$y - 4 z = 0$

$x = 4 y - 5 z$

Subtract $y$ from both sides of the equation.

$- 4 z = - y$

$x = 4 y - 5 z$

Divide each term in $- 4 z = - y$ by $- 4$ and simplify.

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Divide each term in $- 4 z = - y$ by $- 4$ .

$\frac{- 4 z}{- 4} = \frac{- y}{- 4}$

$x = 4 y - 5 z$

Simplify the left side.

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Cancel the common factor of $- 4$ .

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Cancel the common factor.

$\frac{- 4 z}{- 4} = \frac{- y}{- 4}$

$x = 4 y - 5 z$

Divide $z$ by $1$ .

$z = \frac{- y}{- 4}$

$x = 4 y - 5 z$

$z = \frac{- y}{- 4}$

$x = 4 y - 5 z$

$z = \frac{- y}{- 4}$

$x = 4 y - 5 z$

Simplify the right side.

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Dividing two negative values results in a positive value.

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

$x = 4 y - 5 z$

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

$x = 4 y - 5 z$

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

$x = 4 y - 5 z$

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

$x = 4 y - 5 z$

Step 3

Solve the equation for $y$ .

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Combine the opposite terms in $(4 y - 5 \frac{y}{4}) - 4 y + 5 (\frac{y}{4})$ .

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Subtract $4 y$ from $4 y$ .

$- 5 \frac{y}{4} + 0 + 5 (\frac{y}{4}) = 0$

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

Add $- 5 \frac{y}{4}$ and $0$ .

$- 5 \frac{y}{4} + 5 (\frac{y}{4}) = 0$

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

Add $- 5 \frac{y}{4}$ and $5 (\frac{y}{4})$ .

$0 = 0$

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

$0 = 0$

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

Since $0 = 0$ , the equation will always be true.

Always true

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

Always true

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

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