Solve the System of Equations -4x+y-z=12 -5x+y+4z=21 -4x-y+4z=23

$- 4 x + y - z = 12$ $- 5 x + y + 4 z = 21$ $- 4 x - y + 4 z = 23$

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

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

$y - z = 12 + 4 x$

$- 5 x + y + 4 z = 21$

$- 4 x - y + 4 z = 23$

Add $z$ to both sides of the equation.

$y = 12 + 4 x + z$

$- 5 x + y + 4 z = 21$

$- 4 x - y + 4 z = 23$

$y = 12 + 4 x + z$

$- 5 x + y + 4 z = 21$

$- 4 x - y + 4 z = 23$

Replace all occurrences of $y$ with $12 + 4 x + z$ in each equation.

Replace all occurrences of $y$ in $- 5 x + y + 4 z = 21$ with $12 + 4 x + z$ .

$- 5 x + 12 + 4 x + z + 4 z = 21$

$y = 12 + 4 x + z$

$- 4 x - y + 4 z = 23$

Simplify the left side.

Simplify $- 5 x + 12 + 4 x + z + 4 z$ .

Remove parentheses.

$- 5 x + 12 + 4 x + z + 4 z = 21$

$y = 12 + 4 x + z$

$- 4 x - y + 4 z = 23$

Add $- 5 x$ and $4 x$ .

$- x + 12 + z + 4 z = 21$

$y = 12 + 4 x + z$

$- 4 x - y + 4 z = 23$

Add $z$ and $4 z$ .

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$- 4 x - y + 4 z = 23$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$- 4 x - y + 4 z = 23$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$- 4 x - y + 4 z = 23$

Replace all occurrences of $y$ in $- 4 x - y + 4 z = 23$ with $12 + 4 x + z$ .

$- 4 x - (12 + 4 x + z) + 4 z = 23$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

Simplify the left side.

Simplify $- 4 x - (12 + 4 x + z) + 4 z$ .

Simplify each term.

Apply the distributive property.

$- 4 x - 1 \cdot 12 - (4 x) - z + 4 z = 23$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

Simplify.

Multiply $- 1$ by $12$ .

$- 4 x - 12 - (4 x) - z + 4 z = 23$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

Multiply $4$ by $- 1$ .

$- 4 x - 12 - 4 x - z + 4 z = 23$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$- 4 x - 12 - 4 x - z + 4 z = 23$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$- 4 x - 12 - 4 x - z + 4 z = 23$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

Simplify by adding terms.

Subtract $4 x$ from $- 4 x$ .

$- 8 x - 12 - z + 4 z = 23$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

Add $- z$ and $4 z$ .

$- 8 x - 12 + 3 z = 23$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$- 8 x - 12 + 3 z = 23$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$- 8 x - 12 + 3 z = 23$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$- 8 x - 12 + 3 z = 23$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$- 8 x - 12 + 3 z = 23$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

Solve for $x$ in $- 8 x - 12 + 3 z = 23$ .

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

Add $12$ to both sides of the equation.

$- 8 x + 3 z = 23 + 12$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

Subtract $3 z$ from both sides of the equation.

$- 8 x = 23 + 12 - 3 z$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

Add $23$ and $12$ .

$- 8 x = 35 - 3 z$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$- 8 x = 35 - 3 z$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

Divide each term in $- 8 x = 35 - 3 z$ by $- 8$ and simplify.

Divide each term in $- 8 x = 35 - 3 z$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{35}{- 8} + \frac{- 3 z}{- 8}$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{35}{- 8} + \frac{- 3 z}{- 8}$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

Divide $x$ by $1$ .

$x = \frac{35}{- 8} + \frac{- 3 z}{- 8}$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$x = \frac{35}{- 8} + \frac{- 3 z}{- 8}$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$x = \frac{35}{- 8} + \frac{- 3 z}{- 8}$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{35}{8} + \frac{- 3 z}{- 8}$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

Dividing two negative values results in a positive value.

$x = - \frac{35}{8} + \frac{3 z}{8}$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$- x + 12 + 5 z = 21$

$y = 12 + 4 x + z$

Replace all occurrences of $x$ with $- \frac{35}{8} + \frac{3 z}{8}$ in each equation.

Replace all occurrences of $x$ in $- x + 12 + 5 z = 21$ with $- \frac{35}{8} + \frac{3 z}{8}$ .

$- (- \frac{35}{8} + \frac{3 z}{8}) + 12 + 5 z = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

Simplify the left side.

Simplify $- (- \frac{35}{8} + \frac{3 z}{8}) + 12 + 5 z$ .

Simplify each term.

Apply the distributive property.

$\frac{35}{8} - \frac{3 z}{8} + 12 + 5 z = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

Multiply $- - \frac{35}{8}$ .

Multiply $- 1$ by $- 1$ .

$1 (\frac{35}{8}) - \frac{3 z}{8} + 12 + 5 z = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

Multiply $\frac{35}{8}$ by $1$ .

$\frac{35}{8} - \frac{3 z}{8} + 12 + 5 z = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

$\frac{35}{8} - \frac{3 z}{8} + 12 + 5 z = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

$\frac{35}{8} - \frac{3 z}{8} + 12 + 5 z = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

To write $12$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- \frac{3 z}{8} + \frac{35}{8} + 12 \cdot \frac{8}{8} + 5 z = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

Combine $12$ and $\frac{8}{8}$ .

$- \frac{3 z}{8} + \frac{35}{8} + \frac{12 \cdot 8}{8} + 5 z = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

Combine the numerators over the common denominator.

$- \frac{3 z}{8} + \frac{35 + 12 \cdot 8}{8} + 5 z = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

Simplify the numerator.

Multiply $12$ by $8$ .

$- \frac{3 z}{8} + \frac{35 + 96}{8} + 5 z = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

Add $35$ and $96$ .

$- \frac{3 z}{8} + \frac{131}{8} + 5 z = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

$- \frac{3 z}{8} + \frac{131}{8} + 5 z = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

To write $5 z$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- \frac{3 z}{8} + 5 z \cdot \frac{8}{8} + \frac{131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

Combine $5 z$ and $\frac{8}{8}$ .

$- \frac{3 z}{8} + \frac{5 z \cdot 8}{8} + \frac{131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

Combine the numerators over the common denominator.

$\frac{- 3 z + 5 z \cdot 8}{8} + \frac{131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

Combine the numerators over the common denominator.

$\frac{- 3 z + 5 z \cdot 8 + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

Multiply $8$ by $5$ .

$\frac{- 3 z + 40 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

Add $- 3 z$ and $40 z$ .

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + 4 x + z$

Replace all occurrences of $x$ in $y = 12 + 4 x + z$ with $- \frac{35}{8} + \frac{3 z}{8}$ .

$y = 12 + 4 (- \frac{35}{8} + \frac{3 z}{8}) + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Simplify the right side.

Simplify $12 + 4 (- \frac{35}{8} + \frac{3 z}{8}) + z$ .

Simplify each term.

Apply the distributive property.

$y = 12 + 4 (- \frac{35}{8}) + 4 (\frac{3 z}{8}) + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{35}{8}$ into the numerator.

$y = 12 + 4 (\frac{- 35}{8}) + 4 (\frac{3 z}{8}) + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Factor $4$ out of $8$ .

$y = 12 + 4 (\frac{- 35}{4 (2)}) + 4 (\frac{3 z}{8}) + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Cancel the common factor.

$y = 12 + 4 (\frac{- 35}{4 \cdot 2}) + 4 (\frac{3 z}{8}) + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Rewrite the expression.

$y = 12 + \frac{- 35}{2} + 4 (\frac{3 z}{8}) + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + \frac{- 35}{2} + 4 (\frac{3 z}{8}) + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$y = 12 + \frac{- 35}{2} + 4 (\frac{3 z}{4 (2)}) + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Cancel the common factor.

$y = 12 + \frac{- 35}{2} + 4 (\frac{3 z}{4 \cdot 2}) + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Rewrite the expression.

$y = 12 + \frac{- 35}{2} + \frac{3 z}{2} + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 + \frac{- 35}{2} + \frac{3 z}{2} + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Move the negative in front of the fraction.

$y = 12 - \frac{35}{2} + \frac{3 z}{2} + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = 12 - \frac{35}{2} + \frac{3 z}{2} + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

To write $12$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = 12 \cdot \frac{2}{2} - \frac{35}{2} + \frac{3 z}{2} + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Combine $12$ and $\frac{2}{2}$ .

$y = \frac{12 \cdot 2}{2} - \frac{35}{2} + \frac{3 z}{2} + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Combine the numerators over the common denominator.

$y = \frac{12 \cdot 2 - 35}{2} + \frac{3 z}{2} + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Simplify the numerator.

Multiply $12$ by $2$ .

$y = \frac{24 - 35}{2} + \frac{3 z}{2} + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Subtract $35$ from $24$ .

$y = \frac{- 11}{2} + \frac{3 z}{2} + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = \frac{- 11}{2} + \frac{3 z}{2} + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Move the negative in front of the fraction.

$y = - \frac{11}{2} + \frac{3 z}{2} + z$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

To write $z$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{11}{2} + \frac{3 z}{2} + z \cdot \frac{2}{2}$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Simplify terms.

Combine $z$ and $\frac{2}{2}$ .

$y = - \frac{11}{2} + \frac{3 z}{2} + \frac{z \cdot 2}{2}$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Combine the numerators over the common denominator.

$y = - \frac{11}{2} + \frac{3 z + z \cdot 2}{2}$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Combine the numerators over the common denominator.

$y = \frac{- 11 + 3 z + z \cdot 2}{2}$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = \frac{- 11 + 3 z + z \cdot 2}{2}$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Move $2$ to the left of $z$ .

$y = \frac{- 11 + 3 z + 2 z}{2}$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Simplify terms.

Add $3 z$ and $2 z$ .

$y = \frac{- 11 + 5 z}{2}$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Rewrite $- 11$ as $- 1 (11)$ .

$y = \frac{- 1 \cdot 11 + 5 z}{2}$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Factor $- 1$ out of $5 z$ .

$y = \frac{- 1 \cdot 11 - (- 5 z)}{2}$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Factor $- 1$ out of $- 1 (11) - (- 5 z)$ .

$y = \frac{- 1 (11 - 5 z)}{2}$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Move the negative in front of the fraction.

$y = - \frac{11 - 5 z}{2}$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = - \frac{11 - 5 z}{2}$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = - \frac{11 - 5 z}{2}$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = - \frac{11 - 5 z}{2}$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = - \frac{11 - 5 z}{2}$

$\frac{37 z + 131}{8} = 21$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Solve for $z$ in $\frac{37 z + 131}{8} = 21$ .

Multiply both sides by $8$ .

$\frac{37 z + 131}{8} \cdot 8 = 21 \cdot 8$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Simplify.

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{37 z + 131}{8} \cdot 8 = 21 \cdot 8$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Rewrite the expression.

$37 z + 131 = 21 \cdot 8$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$37 z + 131 = 21 \cdot 8$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$37 z + 131 = 21 \cdot 8$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Simplify the right side.

Multiply $21$ by $8$ .

$37 z + 131 = 168$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$37 z + 131 = 168$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$37 z + 131 = 168$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Solve for $z$ .

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

Subtract $131$ from both sides of the equation.

$37 z = 168 - 131$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Subtract $131$ from $168$ .

$37 z = 37$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$37 z = 37$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Divide each term in $37 z = 37$ by $37$ and simplify.

Divide each term in $37 z = 37$ by $37$ .

$\frac{37 z}{37} = \frac{37}{37}$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Simplify the left side.

Cancel the common factor of $37$ .

Cancel the common factor.

$\frac{37 z}{37} = \frac{37}{37}$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Divide $z$ by $1$ .

$z = \frac{37}{37}$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$z = \frac{37}{37}$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$z = \frac{37}{37}$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Simplify the right side.

Divide $37$ by $37$ .

$z = 1$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$z = 1$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$z = 1$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$z = 1$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$z = 1$

$y = - \frac{11 - 5 z}{2}$

$x = - \frac{35}{8} + \frac{3 z}{8}$

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

Replace all occurrences of $z$ in $y = - \frac{11 - 5 z}{2}$ with $1$ .

$y = - \frac{11 - 5 \cdot 1}{2}$

$z = 1$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Simplify the right side.

Simplify $- \frac{11 - 5 \cdot 1}{2}$ .

Simplify the numerator.

Multiply $- 5$ by $1$ .

$y = - \frac{11 - 5}{2}$

$z = 1$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Subtract $5$ from $11$ .

$y = - \frac{6}{2}$

$z = 1$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = - \frac{6}{2}$

$z = 1$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Simplify the expression.

Divide $6$ by $2$ .

$y = - 1 \cdot 3$

$z = 1$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Multiply $- 1$ by $3$ .

$y = - 3$

$z = 1$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = - 3$

$z = 1$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = - 3$

$z = 1$

$x = - \frac{35}{8} + \frac{3 z}{8}$

$y = - 3$

$z = 1$

$x = - \frac{35}{8} + \frac{3 z}{8}$

Replace all occurrences of $z$ in $x = - \frac{35}{8} + \frac{3 z}{8}$ with $1$ .

$x = - \frac{35}{8} + \frac{3 (1)}{8}$

$y = - 3$

$z = 1$

Simplify the right side.

Simplify $- \frac{35}{8} + \frac{3 (1)}{8}$ .

Combine the numerators over the common denominator.

$x = \frac{- 35 + 3 (1)}{8}$

$y = - 3$

$z = 1$

Simplify the expression.

Multiply $3$ by $1$ .

$x = \frac{- 35 + 3}{8}$

$y = - 3$

$z = 1$

Add $- 35$ and $3$ .

$x = \frac{- 32}{8}$

$y = - 3$

$z = 1$

Divide $- 32$ by $8$ .

$x = - 4$

$y = - 3$

$z = 1$

$x = - 4$

$y = - 3$

$z = 1$

$x = - 4$

$y = - 3$

$z = 1$

$x = - 4$

$y = - 3$

$z = 1$

$x = - 4$

$y = - 3$

$z = 1$

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

$(- 4, - 3, 1)$

The result can be shown in multiple forms.

Point Form:

$(- 4, - 3, 1)$

Equation Form:

$x = - 4, y = - 3, z = 1$

Solve the System of Equations -4x+y-z=12 -5x+y+4z=21 -4x-y+4z=23

Related Questions

Support LCMGCF.com by disabling your adblocker.