Finite Math Examples

$- 0.4 x + 0.3 y + 0.2 z = 0$ , $0.2 x - 0.4 y + 0.7 z = 0$ , $0.2 x + 0.1 y - 0.9 z = 0$ , $x + y + z = 1$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $y$ from both sides of the equation.

$x + z = 1 - y$

$- 0.4 x + 0.3 y + 0.2 z = 0$

$0.2 x - 0.4 y + 0.7 z = 0$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 1.2

Subtract $z$ from both sides of the equation.

$x = 1 - y - z$

$- 0.4 x + 0.3 y + 0.2 z = 0$

$0.2 x - 0.4 y + 0.7 z = 0$

$0.2 x + 0.1 y - 0.9 z = 0$

$x = 1 - y - z$

$- 0.4 x + 0.3 y + 0.2 z = 0$

$0.2 x - 0.4 y + 0.7 z = 0$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 2

Replace all occurrences of $x$ with $1 - y - z$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $- 0.4 x + 0.3 y + 0.2 z = 0$ with $1 - y - z$ .

$- 0.4 (1 - y - z) + 0.3 y + 0.2 z = 0$

$x = 1 - y - z$

$0.2 x - 0.4 y + 0.7 z = 0$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $- 0.4 (1 - y - z) + 0.3 y + 0.2 z$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

$- 0.4 \cdot 1 - 0.4 (- y) - 0.4 (- z) + 0.3 y + 0.2 z = 0$

$x = 1 - y - z$

$0.2 x - 0.4 y + 0.7 z = 0$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 2.2.1.1.2

Simplify.

Tap for more steps...

Step 2.2.1.1.2.1

Multiply $- 0.4$ by $1$ .

$- 0.4 - 0.4 (- y) - 0.4 (- z) + 0.3 y + 0.2 z = 0$

$x = 1 - y - z$

$0.2 x - 0.4 y + 0.7 z = 0$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 2.2.1.1.2.2

Multiply $- 1$ by $- 0.4$ .

$- 0.4 + 0.4 y - 0.4 (- z) + 0.3 y + 0.2 z = 0$

$x = 1 - y - z$

$0.2 x - 0.4 y + 0.7 z = 0$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 2.2.1.1.2.3

Multiply $- 1$ by $- 0.4$ .

$- 0.4 + 0.4 y + 0.4 z + 0.3 y + 0.2 z = 0$

$x = 1 - y - z$

$0.2 x - 0.4 y + 0.7 z = 0$

$0.2 x + 0.1 y - 0.9 z = 0$

$- 0.4 + 0.4 y + 0.4 z + 0.3 y + 0.2 z = 0$

$x = 1 - y - z$

$0.2 x - 0.4 y + 0.7 z = 0$

$0.2 x + 0.1 y - 0.9 z = 0$

$- 0.4 + 0.4 y + 0.4 z + 0.3 y + 0.2 z = 0$

$x = 1 - y - z$

$0.2 x - 0.4 y + 0.7 z = 0$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 2.2.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.2.1.2.1

Add $0.4 y$ and $0.3 y$ .

$- 0.4 + 0.7 y + 0.4 z + 0.2 z = 0$

$x = 1 - y - z$

$0.2 x - 0.4 y + 0.7 z = 0$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 2.2.1.2.2

Add $0.4 z$ and $0.2 z$ .

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x - 0.4 y + 0.7 z = 0$

$0.2 x + 0.1 y - 0.9 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x - 0.4 y + 0.7 z = 0$

$0.2 x + 0.1 y - 0.9 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x - 0.4 y + 0.7 z = 0$

$0.2 x + 0.1 y - 0.9 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x - 0.4 y + 0.7 z = 0$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 2.3

Replace all occurrences of $x$ in $0.2 x - 0.4 y + 0.7 z = 0$ with $1 - y - z$ .

$0.2 (1 - y - z) - 0.4 y + 0.7 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 2.4

Simplify the left side.

Tap for more steps...

Step 2.4.1

Simplify $0.2 (1 - y - z) - 0.4 y + 0.7 z$ .

Tap for more steps...

Step 2.4.1.1

Simplify each term.

Tap for more steps...

Step 2.4.1.1.1

Apply the distributive property.

$0.2 \cdot 1 + 0.2 (- y) + 0.2 (- z) - 0.4 y + 0.7 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 2.4.1.1.2

Simplify.

Tap for more steps...

Step 2.4.1.1.2.1

Multiply $0.2$ by $1$ .

$0.2 + 0.2 (- y) + 0.2 (- z) - 0.4 y + 0.7 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 2.4.1.1.2.2

Multiply $- 1$ by $0.2$ .

$0.2 - 0.2 y + 0.2 (- z) - 0.4 y + 0.7 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 2.4.1.1.2.3

Multiply $- 1$ by $0.2$ .

$0.2 - 0.2 y - 0.2 z - 0.4 y + 0.7 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x + 0.1 y - 0.9 z = 0$

$0.2 - 0.2 y - 0.2 z - 0.4 y + 0.7 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x + 0.1 y - 0.9 z = 0$

$0.2 - 0.2 y - 0.2 z - 0.4 y + 0.7 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 2.4.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.4.1.2.1

Subtract $0.4 y$ from $- 0.2 y$ .

$0.2 - 0.6 y - 0.2 z + 0.7 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 2.4.1.2.2

Add $- 0.2 z$ and $0.7 z$ .

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x + 0.1 y - 0.9 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x + 0.1 y - 0.9 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x + 0.1 y - 0.9 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 x + 0.1 y - 0.9 z = 0$

Step 2.5

Replace all occurrences of $x$ in $0.2 x + 0.1 y - 0.9 z = 0$ with $1 - y - z$ .

$0.2 (1 - y - z) + 0.1 y - 0.9 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 2.6

Simplify the left side.

Tap for more steps...

Step 2.6.1

Simplify $0.2 (1 - y - z) + 0.1 y - 0.9 z$ .

Tap for more steps...

Step 2.6.1.1

Simplify each term.

Tap for more steps...

Step 2.6.1.1.1

Apply the distributive property.

$0.2 \cdot 1 + 0.2 (- y) + 0.2 (- z) + 0.1 y - 0.9 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 2.6.1.1.2

Simplify.

Tap for more steps...

Step 2.6.1.1.2.1

Multiply $0.2$ by $1$ .

$0.2 + 0.2 (- y) + 0.2 (- z) + 0.1 y - 0.9 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 2.6.1.1.2.2

Multiply $- 1$ by $0.2$ .

$0.2 - 0.2 y + 0.2 (- z) + 0.1 y - 0.9 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 2.6.1.1.2.3

Multiply $- 1$ by $0.2$ .

$0.2 - 0.2 y - 0.2 z + 0.1 y - 0.9 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 - 0.2 y - 0.2 z + 0.1 y - 0.9 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 - 0.2 y - 0.2 z + 0.1 y - 0.9 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 2.6.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.6.1.2.1

Add $- 0.2 y$ and $0.1 y$ .

$0.2 - 0.1 y - 0.2 z - 0.9 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 2.6.1.2.2

Subtract $0.9 z$ from $- 0.2 z$ .

$0.2 - 0.1 y - 1.1 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 - 0.1 y - 1.1 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 - 0.1 y - 1.1 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 - 0.1 y - 1.1 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 - 0.1 y - 1.1 z = 0$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 3

Solve for $y$ in $0.2 - 0.1 y - 1.1 z = 0$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Subtract $0.2$ from both sides of the equation.

$- 0.1 y - 1.1 z = - 0.2$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 3.1.2

Add $1.1 z$ to both sides of the equation.

$- 0.1 y = - 0.2 + 1.1 z$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$- 0.1 y = - 0.2 + 1.1 z$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 3.2

Divide each term in $- 0.1 y = - 0.2 + 1.1 z$ by $- 0.1$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $- 0.1 y = - 0.2 + 1.1 z$ by $- 0.1$ .

$\frac{- 0.1 y}{- 0.1} = \frac{- 0.2}{- 0.1} + \frac{1.1 z}{- 0.1}$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $- 0.1$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 0.1 y}{- 0.1} = \frac{- 0.2}{- 0.1} + \frac{1.1 z}{- 0.1}$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 0.2}{- 0.1} + \frac{1.1 z}{- 0.1}$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$y = \frac{- 0.2}{- 0.1} + \frac{1.1 z}{- 0.1}$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$y = \frac{- 0.2}{- 0.1} + \frac{1.1 z}{- 0.1}$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Simplify each term.

Tap for more steps...

Step 3.2.3.1.1

Divide $- 0.2$ by $- 0.1$ .

$y = 2 + \frac{1.1 z}{- 0.1}$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 3.2.3.1.2

Move the negative in front of the fraction.

$y = 2 - \frac{1.1 z}{0.1}$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 3.2.3.1.3

Factor $1.1$ out of $1.1 z$ .

$y = 2 - \frac{1.1 (z)}{0.1}$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 3.2.3.1.4

Factor $0.1$ out of $0.1$ .

$y = 2 - \frac{1.1 (z)}{0.1 (1)}$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 3.2.3.1.5

Separate fractions.

$y = 2 - (\frac{1.1}{0.1} \cdot \frac{z}{1})$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 3.2.3.1.6

Divide $1.1$ by $0.1$ .

$y = 2 - (11 (\frac{z}{1}))$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 3.2.3.1.7

Divide $z$ by $1$ .

$y = 2 - (11 z)$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 3.2.3.1.8

Multiply $11$ by $- 1$ .

$y = 2 - 11 z$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$y = 2 - 11 z$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$y = 2 - 11 z$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$y = 2 - 11 z$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$y = 2 - 11 z$

$0.2 - 0.6 y + 0.5 z = 0$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 4

Replace all occurrences of $y$ with $2 - 11 z$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of $y$ in $0.2 - 0.6 y + 0.5 z = 0$ with $2 - 11 z$ .

$0.2 - 0.6 (2 - 11 z) + 0.5 z = 0$

$y = 2 - 11 z$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Simplify $0.2 - 0.6 (2 - 11 z) + 0.5 z$ .

Tap for more steps...

Step 4.2.1.1

Simplify each term.

Tap for more steps...

Step 4.2.1.1.1

Apply the distributive property.

$0.2 - 0.6 \cdot 2 - 0.6 (- 11 z) + 0.5 z = 0$

$y = 2 - 11 z$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 4.2.1.1.2

Multiply $- 0.6$ by $2$ .

$0.2 - 1.2 - 0.6 (- 11 z) + 0.5 z = 0$

$y = 2 - 11 z$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 4.2.1.1.3

Multiply $- 11$ by $- 0.6$ .

$0.2 - 1.2 + 6.6 z + 0.5 z = 0$

$y = 2 - 11 z$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$0.2 - 1.2 + 6.6 z + 0.5 z = 0$

$y = 2 - 11 z$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 4.2.1.2

Simplify by adding terms.

Tap for more steps...

Step 4.2.1.2.1

Subtract $1.2$ from $0.2$ .

$- 1 + 6.6 z + 0.5 z = 0$

$y = 2 - 11 z$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 4.2.1.2.2

Add $6.6 z$ and $0.5 z$ .

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$- 0.4 + 0.7 y + 0.6 z = 0$

$x = 1 - y - z$

Step 4.3

Replace all occurrences of $y$ in $- 0.4 + 0.7 y + 0.6 z = 0$ with $2 - 11 z$ .

$- 0.4 + 0.7 (2 - 11 z) + 0.6 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = 1 - y - z$

Step 4.4

Simplify the left side.

Tap for more steps...

Step 4.4.1

Simplify $- 0.4 + 0.7 (2 - 11 z) + 0.6 z$ .

Tap for more steps...

Step 4.4.1.1

Simplify each term.

Tap for more steps...

Step 4.4.1.1.1

Apply the distributive property.

$- 0.4 + 0.7 \cdot 2 + 0.7 (- 11 z) + 0.6 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = 1 - y - z$

Step 4.4.1.1.2

Multiply $0.7$ by $2$ .

$- 0.4 + 1.4 + 0.7 (- 11 z) + 0.6 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = 1 - y - z$

Step 4.4.1.1.3

Multiply $- 11$ by $0.7$ .

$- 0.4 + 1.4 - 7.7 z + 0.6 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = 1 - y - z$

$- 0.4 + 1.4 - 7.7 z + 0.6 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = 1 - y - z$

Step 4.4.1.2

Simplify by adding terms.

Tap for more steps...

Step 4.4.1.2.1

Add $- 0.4$ and $1.4$ .

$1 - 7.7 z + 0.6 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = 1 - y - z$

Step 4.4.1.2.2

Add $- 7.7 z$ and $0.6 z$ .

$1 - 7.1 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = 1 - y - z$

$1 - 7.1 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = 1 - y - z$

$1 - 7.1 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = 1 - y - z$

$1 - 7.1 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = 1 - y - z$

Step 4.5

Replace all occurrences of $y$ in $x = 1 - y - z$ with $2 - 11 z$ .

$x = 1 - (2 - 11 z) - z$

$1 - 7.1 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

Step 4.6

Simplify the right side.

Tap for more steps...

Step 4.6.1

Simplify $1 - (2 - 11 z) - z$ .

Tap for more steps...

Step 4.6.1.1

Simplify each term.

Tap for more steps...

Step 4.6.1.1.1

Apply the distributive property.

$x = 1 - 1 \cdot 2 - (- 11 z) - z$

$1 - 7.1 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

Step 4.6.1.1.2

Multiply $- 1$ by $2$ .

$x = 1 - 2 - (- 11 z) - z$

$1 - 7.1 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

Step 4.6.1.1.3

Multiply $- 11$ by $- 1$ .

$x = 1 - 2 + 11 z - z$

$1 - 7.1 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = 1 - 2 + 11 z - z$

$1 - 7.1 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

Step 4.6.1.2

Simplify by adding terms.

Tap for more steps...

Step 4.6.1.2.1

Subtract $2$ from $1$ .

$x = - 1 + 11 z - z$

$1 - 7.1 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

Step 4.6.1.2.2

Subtract $z$ from $11 z$ .

$x = - 1 + 10 z$

$1 - 7.1 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = - 1 + 10 z$

$1 - 7.1 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = - 1 + 10 z$

$1 - 7.1 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = - 1 + 10 z$

$1 - 7.1 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = - 1 + 10 z$

$1 - 7.1 z = 0$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

Step 5

Solve for $z$ in $1 - 7.1 z = 0$ .

Tap for more steps...

Step 5.1

Subtract $1$ from both sides of the equation.

$- 7.1 z = - 1$

$x = - 1 + 10 z$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

Step 5.2

Divide each term in $- 7.1 z = - 1$ by $- 7.1$ and simplify.

Tap for more steps...

Step 5.2.1

Divide each term in $- 7.1 z = - 1$ by $- 7.1$ .

$\frac{- 7.1 z}{- 7.1} = \frac{- 1}{- 7.1}$

$x = - 1 + 10 z$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

Step 5.2.2

Simplify the left side.

Tap for more steps...

Step 5.2.2.1

Cancel the common factor of $- 7.1$ .

Tap for more steps...

Step 5.2.2.1.1

Cancel the common factor.

$\frac{- 7.1 z}{- 7.1} = \frac{- 1}{- 7.1}$

$x = - 1 + 10 z$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

Step 5.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{- 1}{- 7.1}$

$x = - 1 + 10 z$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$z = \frac{- 1}{- 7.1}$

$x = - 1 + 10 z$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$z = \frac{- 1}{- 7.1}$

$x = - 1 + 10 z$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

Step 5.2.3

Simplify the right side.

Tap for more steps...

Step 5.2.3.1

Divide $- 1$ by $- 7.1$ .

$z = 0.14084507$

$x = - 1 + 10 z$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$z = 0.14084507$

$x = - 1 + 10 z$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$z = 0.14084507$

$x = - 1 + 10 z$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$z = 0.14084507$

$x = - 1 + 10 z$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

Step 6

Replace all occurrences of $z$ with $0.14084507$ in each equation.

Tap for more steps...

Step 6.1

Replace all occurrences of $z$ in $x = - 1 + 10 z$ with $0.14084507$ .

$x = - 1 + 10 (0.14084507)$

$z = 0.14084507$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Simplify $- 1 + 10 (0.14084507)$ .

Tap for more steps...

Step 6.2.1.1

Multiply $10$ by $0.14084507$ .

$x = - 1 + 1.4084507$

$z = 0.14084507$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

Step 6.2.1.2

Add $- 1$ and $1.4084507$ .

$x = 0.4084507$

$z = 0.14084507$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = 0.4084507$

$z = 0.14084507$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

$x = 0.4084507$

$z = 0.14084507$

$- 1 + 7.1 z = 0$

$y = 2 - 11 z$

Step 6.3

Replace all occurrences of $z$ in $- 1 + 7.1 z = 0$ with $0.14084507$ .

$- 1 + 7.1 (0.14084507) = 0$

$x = 0.4084507$

$z = 0.14084507$

$y = 2 - 11 z$

Step 6.4

Simplify the left side.

Tap for more steps...

Step 6.4.1

Simplify $- 1 + 7.1 (0.14084507)$ .

Tap for more steps...

Step 6.4.1.1

Multiply $7.1$ by $0.14084507$ .

$- 1 + 1 = 0$

$x = 0.4084507$

$z = 0.14084507$

$y = 2 - 11 z$

Step 6.4.1.2

Add $- 1$ and $1$ .

$0 = 0$

$x = 0.4084507$

$z = 0.14084507$

$y = 2 - 11 z$

$0 = 0$

$x = 0.4084507$

$z = 0.14084507$

$y = 2 - 11 z$

$0 = 0$

$x = 0.4084507$

$z = 0.14084507$

$y = 2 - 11 z$

Step 6.5

Replace all occurrences of $z$ in $y = 2 - 11 z$ with $0.14084507$ .

$y = 2 - 11 \cdot 0.14084507$

$0 = 0$

$x = 0.4084507$

$z = 0.14084507$

Step 6.6

Simplify the right side.

Tap for more steps...

Step 6.6.1

Simplify $2 - 11 \cdot 0.14084507$ .

Tap for more steps...

Step 6.6.1.1

Multiply $- 11$ by $0.14084507$ .

$y = 2 - 1.54929577$

$0 = 0$

$x = 0.4084507$

$z = 0.14084507$

Step 6.6.1.2

Subtract $1.54929577$ from $2$ .

$y = 0.45070422$

$0 = 0$

$x = 0.4084507$

$z = 0.14084507$

$y = 0.45070422$

$0 = 0$

$x = 0.4084507$

$z = 0.14084507$

$y = 0.45070422$

$0 = 0$

$x = 0.4084507$

$z = 0.14084507$

$y = 0.45070422$

$0 = 0$

$x = 0.4084507$

$z = 0.14084507$

Step 7

Remove any equations from the system that are always true.

$y = 0.45070422$

$x = 0.4084507$

$z = 0.14084507$

Step 8

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(0.4084507, 0.45070422, 0.14084507)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(0.4084507, 0.45070422, 0.14084507)$

Equation Form:

$x = 0.4084507, y = 0.45070422, z = 0.14084507$