Solve the System of Equations 9x+3y-4z=37 4x+3y+7z=16 x-5y+8z=-31

$9 x + 3 y - 4 z = 37$ $4 x + 3 y + 7 z = 16$ $x - 5 y + 8 z = - 31$

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

Add $5 y$ to both sides of the equation.

$x + 8 z = - 31 + 5 y$

$9 x + 3 y - 4 z = 37$

$4 x + 3 y + 7 z = 16$

Subtract $8 z$ from both sides of the equation.

$x = - 31 + 5 y - 8 z$

$9 x + 3 y - 4 z = 37$

$4 x + 3 y + 7 z = 16$

$x = - 31 + 5 y - 8 z$

$9 x + 3 y - 4 z = 37$

$4 x + 3 y + 7 z = 16$

Replace all occurrences of $x$ with $- 31 + 5 y - 8 z$ in each equation.

Replace all occurrences of $x$ in $9 x + 3 y - 4 z = 37$ with $- 31 + 5 y - 8 z$ .

$9 (- 31 + 5 y - 8 z) + 3 y - 4 z = 37$

$x = - 31 + 5 y - 8 z$

$4 x + 3 y + 7 z = 16$

Simplify the left side.

Simplify $9 (- 31 + 5 y - 8 z) + 3 y - 4 z$ .

Simplify each term.

Apply the distributive property.

$9 \cdot - 31 + 9 (5 y) + 9 (- 8 z) + 3 y - 4 z = 37$

$x = - 31 + 5 y - 8 z$

$4 x + 3 y + 7 z = 16$

Simplify.

Multiply $9$ by $- 31$ .

$- 279 + 9 (5 y) + 9 (- 8 z) + 3 y - 4 z = 37$

$x = - 31 + 5 y - 8 z$

$4 x + 3 y + 7 z = 16$

Multiply $5$ by $9$ .

$- 279 + 45 y + 9 (- 8 z) + 3 y - 4 z = 37$

$x = - 31 + 5 y - 8 z$

$4 x + 3 y + 7 z = 16$

Multiply $- 8$ by $9$ .

$- 279 + 45 y - 72 z + 3 y - 4 z = 37$

$x = - 31 + 5 y - 8 z$

$4 x + 3 y + 7 z = 16$

$- 279 + 45 y - 72 z + 3 y - 4 z = 37$

$x = - 31 + 5 y - 8 z$

$4 x + 3 y + 7 z = 16$

$- 279 + 45 y - 72 z + 3 y - 4 z = 37$

$x = - 31 + 5 y - 8 z$

$4 x + 3 y + 7 z = 16$

Simplify by adding terms.

Add $45 y$ and $3 y$ .

$- 279 + 48 y - 72 z - 4 z = 37$

$x = - 31 + 5 y - 8 z$

$4 x + 3 y + 7 z = 16$

Subtract $4 z$ from $- 72 z$ .

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

$4 x + 3 y + 7 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

$4 x + 3 y + 7 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

$4 x + 3 y + 7 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

$4 x + 3 y + 7 z = 16$

Replace all occurrences of $x$ in $4 x + 3 y + 7 z = 16$ with $- 31 + 5 y - 8 z$ .

$4 (- 31 + 5 y - 8 z) + 3 y + 7 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

Simplify the left side.

Simplify $4 (- 31 + 5 y - 8 z) + 3 y + 7 z$ .

Simplify each term.

Apply the distributive property.

$4 \cdot - 31 + 4 (5 y) + 4 (- 8 z) + 3 y + 7 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

Simplify.

Multiply $4$ by $- 31$ .

$- 124 + 4 (5 y) + 4 (- 8 z) + 3 y + 7 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

Multiply $5$ by $4$ .

$- 124 + 20 y + 4 (- 8 z) + 3 y + 7 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

Multiply $- 8$ by $4$ .

$- 124 + 20 y - 32 z + 3 y + 7 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

$- 124 + 20 y - 32 z + 3 y + 7 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

$- 124 + 20 y - 32 z + 3 y + 7 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

Simplify by adding terms.

Add $20 y$ and $3 y$ .

$- 124 + 23 y - 32 z + 7 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

Add $- 32 z$ and $7 z$ .

$- 124 + 23 y - 25 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

$- 124 + 23 y - 25 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

$- 124 + 23 y - 25 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

$- 124 + 23 y - 25 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

$- 124 + 23 y - 25 z = 16$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

Solve for $y$ in $- 124 + 23 y - 25 z = 16$ .

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

Add $124$ to both sides of the equation.

$23 y - 25 z = 16 + 124$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

Add $25 z$ to both sides of the equation.

$23 y = 16 + 124 + 25 z$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

Add $16$ and $124$ .

$23 y = 140 + 25 z$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

$23 y = 140 + 25 z$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

Divide each term in $23 y = 140 + 25 z$ by $23$ and simplify.

Divide each term in $23 y = 140 + 25 z$ by $23$ .

$\frac{23 y}{23} = \frac{140}{23} + \frac{25 z}{23}$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

Simplify the left side.

Cancel the common factor of $23$ .

Cancel the common factor.

$\frac{23 y}{23} = \frac{140}{23} + \frac{25 z}{23}$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

Divide $y$ by $1$ .

$y = \frac{140}{23} + \frac{25 z}{23}$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

$y = \frac{140}{23} + \frac{25 z}{23}$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

$y = \frac{140}{23} + \frac{25 z}{23}$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

$y = \frac{140}{23} + \frac{25 z}{23}$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

$y = \frac{140}{23} + \frac{25 z}{23}$

$- 279 + 48 y - 76 z = 37$

$x = - 31 + 5 y - 8 z$

Replace all occurrences of $y$ with $\frac{140}{23} + \frac{25 z}{23}$ in each equation.

Replace all occurrences of $y$ in $- 279 + 48 y - 76 z = 37$ with $\frac{140}{23} + \frac{25 z}{23}$ .

$- 279 + 48 (\frac{140}{23} + \frac{25 z}{23}) - 76 z = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

Simplify the left side.

Simplify $- 279 + 48 (\frac{140}{23} + \frac{25 z}{23}) - 76 z$ .

Simplify each term.

Apply the distributive property.

$- 279 + 48 (\frac{140}{23}) + 48 (\frac{25 z}{23}) - 76 z = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

Multiply $48 (\frac{140}{23})$ .

Combine $48$ and $\frac{140}{23}$ .

$- 279 + \frac{48 \cdot 140}{23} + 48 (\frac{25 z}{23}) - 76 z = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

Multiply $48$ by $140$ .

$- 279 + \frac{6720}{23} + 48 (\frac{25 z}{23}) - 76 z = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

$- 279 + \frac{6720}{23} + 48 (\frac{25 z}{23}) - 76 z = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

Multiply $48 \frac{25 z}{23}$ .

Combine $48$ and $\frac{25 z}{23}$ .

$- 279 + \frac{6720}{23} + \frac{48 (25 z)}{23} - 76 z = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

Multiply $25$ by $48$ .

$- 279 + \frac{6720}{23} + \frac{1200 z}{23} - 76 z = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

$- 279 + \frac{6720}{23} + \frac{1200 z}{23} - 76 z = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

$- 279 + \frac{6720}{23} + \frac{1200 z}{23} - 76 z = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

To write $- 279$ as a fraction with a common denominator, multiply by $\frac{23}{23}$ .

$- 279 \cdot \frac{23}{23} + \frac{6720}{23} + \frac{1200 z}{23} - 76 z = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

Combine $- 279$ and $\frac{23}{23}$ .

$\frac{- 279 \cdot 23}{23} + \frac{6720}{23} + \frac{1200 z}{23} - 76 z = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

Combine the numerators over the common denominator.

$\frac{- 279 \cdot 23 + 6720}{23} + \frac{1200 z}{23} - 76 z = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

Simplify the numerator.

Multiply $- 279$ by $23$ .

$\frac{- 6417 + 6720}{23} + \frac{1200 z}{23} - 76 z = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

Add $- 6417$ and $6720$ .

$\frac{303}{23} + \frac{1200 z}{23} - 76 z = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

$\frac{303}{23} + \frac{1200 z}{23} - 76 z = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

To write $- 76 z$ as a fraction with a common denominator, multiply by $\frac{23}{23}$ .

$\frac{303}{23} + \frac{1200 z}{23} - 76 z \cdot \frac{23}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

Combine $- 76 z$ and $\frac{23}{23}$ .

$\frac{303}{23} + \frac{1200 z}{23} + \frac{- 76 z \cdot 23}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

Combine the numerators over the common denominator.

$\frac{303}{23} + \frac{1200 z - 76 z \cdot 23}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

Combine the numerators over the common denominator.

$\frac{303 + 1200 z - 76 z \cdot 23}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

Multiply $23$ by $- 76$ .

$\frac{303 + 1200 z - 1748 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

Subtract $1748 z$ from $1200 z$ .

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + 5 y - 8 z$

Replace all occurrences of $y$ in $x = - 31 + 5 y - 8 z$ with $\frac{140}{23} + \frac{25 z}{23}$ .

$x = - 31 + 5 (\frac{140}{23} + \frac{25 z}{23}) - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Simplify the right side.

Simplify $- 31 + 5 (\frac{140}{23} + \frac{25 z}{23}) - 8 z$ .

Simplify each term.

Apply the distributive property.

$x = - 31 + 5 (\frac{140}{23}) + 5 (\frac{25 z}{23}) - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Multiply $5 (\frac{140}{23})$ .

Combine $5$ and $\frac{140}{23}$ .

$x = - 31 + \frac{5 \cdot 140}{23} + 5 (\frac{25 z}{23}) - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Multiply $5$ by $140$ .

$x = - 31 + \frac{700}{23} + 5 (\frac{25 z}{23}) - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + \frac{700}{23} + 5 (\frac{25 z}{23}) - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Multiply $5 \frac{25 z}{23}$ .

Combine $5$ and $\frac{25 z}{23}$ .

$x = - 31 + \frac{700}{23} + \frac{5 (25 z)}{23} - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Multiply $25$ by $5$ .

$x = - 31 + \frac{700}{23} + \frac{125 z}{23} - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + \frac{700}{23} + \frac{125 z}{23} - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - 31 + \frac{700}{23} + \frac{125 z}{23} - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

To write $- 31$ as a fraction with a common denominator, multiply by $\frac{23}{23}$ .

$x = - 31 \cdot \frac{23}{23} + \frac{700}{23} + \frac{125 z}{23} - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Combine $- 31$ and $\frac{23}{23}$ .

$x = \frac{- 31 \cdot 23}{23} + \frac{700}{23} + \frac{125 z}{23} - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Combine the numerators over the common denominator.

$x = \frac{- 31 \cdot 23 + 700}{23} + \frac{125 z}{23} - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Simplify the numerator.

Multiply $- 31$ by $23$ .

$x = \frac{- 713 + 700}{23} + \frac{125 z}{23} - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Add $- 713$ and $700$ .

$x = \frac{- 13}{23} + \frac{125 z}{23} - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = \frac{- 13}{23} + \frac{125 z}{23} - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Move the negative in front of the fraction.

$x = - \frac{13}{23} + \frac{125 z}{23} - 8 z$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

To write $- 8 z$ as a fraction with a common denominator, multiply by $\frac{23}{23}$ .

$x = - \frac{13}{23} + \frac{125 z}{23} - 8 z \cdot \frac{23}{23}$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Combine $- 8 z$ and $\frac{23}{23}$ .

$x = - \frac{13}{23} + \frac{125 z}{23} + \frac{- 8 z \cdot 23}{23}$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Combine the numerators over the common denominator.

$x = - \frac{13}{23} + \frac{125 z - 8 z \cdot 23}{23}$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Combine the numerators over the common denominator.

$x = \frac{- 13 + 125 z - 8 z \cdot 23}{23}$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Multiply $23$ by $- 8$ .

$x = \frac{- 13 + 125 z - 184 z}{23}$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Subtract $184 z$ from $125 z$ .

$x = \frac{- 13 - 59 z}{23}$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Rewrite $- 13$ as $- 1 (13)$ .

$x = \frac{- 1 \cdot 13 - 59 z}{23}$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Factor $- 1$ out of $- 59 z$ .

$x = \frac{- 1 \cdot 13 - (59 z)}{23}$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Factor $- 1$ out of $- 1 (13) - (59 z)$ .

$x = \frac{- 1 (13 + 59 z)}{23}$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Move the negative in front of the fraction.

$x = - \frac{13 + 59 z}{23}$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - \frac{13 + 59 z}{23}$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - \frac{13 + 59 z}{23}$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - \frac{13 + 59 z}{23}$

$\frac{303 - 548 z}{23} = 37$

$y = \frac{140}{23} + \frac{25 z}{23}$

Solve for $z$ in $\frac{303 - 548 z}{23} = 37$ .

Multiply both sides by $23$ .

$\frac{303 - 548 z}{23} \cdot 23 = 37 \cdot 23$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

Simplify.

Simplify the left side.

Simplify $\frac{303 - 548 z}{23} \cdot 23$ .

Cancel the common factor of $23$ .

Cancel the common factor.

$\frac{303 - 548 z}{23} \cdot 23 = 37 \cdot 23$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

Rewrite the expression.

$303 - 548 z = 37 \cdot 23$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

$303 - 548 z = 37 \cdot 23$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

Reorder $303$ and $- 548 z$ .

$- 548 z + 303 = 37 \cdot 23$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

$- 548 z + 303 = 37 \cdot 23$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

$- 548 z + 303 = 37 \cdot 23$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

Simplify the right side.

Multiply $37$ by $23$ .

$- 548 z + 303 = 851$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

$- 548 z + 303 = 851$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

$- 548 z + 303 = 851$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

Solve for $z$ .

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

Subtract $303$ from both sides of the equation.

$- 548 z = 851 - 303$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

Subtract $303$ from $851$ .

$- 548 z = 548$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

$- 548 z = 548$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

Divide each term in $- 548 z = 548$ by $- 548$ and simplify.

Divide each term in $- 548 z = 548$ by $- 548$ .

$\frac{- 548 z}{- 548} = \frac{548}{- 548}$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

Simplify the left side.

Cancel the common factor of $- 548$ .

Cancel the common factor.

$\frac{- 548 z}{- 548} = \frac{548}{- 548}$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

Divide $z$ by $1$ .

$z = \frac{548}{- 548}$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

$z = \frac{548}{- 548}$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

$z = \frac{548}{- 548}$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

Simplify the right side.

Divide $548$ by $- 548$ .

$z = - 1$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

$z = - 1$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

$z = - 1$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

$z = - 1$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

$z = - 1$

$x = - \frac{13 + 59 z}{23}$

$y = \frac{140}{23} + \frac{25 z}{23}$

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

Replace all occurrences of $z$ in $x = - \frac{13 + 59 z}{23}$ with $- 1$ .

$x = - \frac{13 + 59 (- 1)}{23}$

$z = - 1$

$y = \frac{140}{23} + \frac{25 z}{23}$

Simplify the right side.

Simplify $- \frac{13 + 59 (- 1)}{23}$ .

Simplify the numerator.

Multiply $59$ by $- 1$ .

$x = - \frac{13 - 59}{23}$

$z = - 1$

$y = \frac{140}{23} + \frac{25 z}{23}$

Subtract $59$ from $13$ .

$x = - \frac{- 46}{23}$

$z = - 1$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = - \frac{- 46}{23}$

$z = - 1$

$y = \frac{140}{23} + \frac{25 z}{23}$

Simplify the expression.

Divide $- 46$ by $23$ .

$x = 2$

$z = - 1$

$y = \frac{140}{23} + \frac{25 z}{23}$

Multiply $- 1$ by $- 2$ .

$x = 2$

$z = - 1$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = 2$

$z = - 1$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = 2$

$z = - 1$

$y = \frac{140}{23} + \frac{25 z}{23}$

$x = 2$

$z = - 1$

$y = \frac{140}{23} + \frac{25 z}{23}$

Replace all occurrences of $z$ in $y = \frac{140}{23} + \frac{25 z}{23}$ with $- 1$ .

$y = \frac{140}{23} + \frac{25 (- 1)}{23}$

$x = 2$

$z = - 1$

Simplify the right side.

Simplify $\frac{140}{23} + \frac{25 (- 1)}{23}$ .

Combine the numerators over the common denominator.

$y = \frac{140 + 25 (- 1)}{23}$

$x = 2$

$z = - 1$

Simplify the expression.

Multiply $25$ by $- 1$ .

$y = \frac{140 - 25}{23}$

$x = 2$

$z = - 1$

Subtract $25$ from $140$ .

$y = \frac{115}{23}$

$x = 2$

$z = - 1$

Divide $115$ by $23$ .

$y = 5$

$x = 2$

$z = - 1$

$y = 5$

$x = 2$

$z = - 1$

$y = 5$

$x = 2$

$z = - 1$

$y = 5$

$x = 2$

$z = - 1$

$y = 5$

$x = 2$

$z = - 1$

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

$(2, 5, - 1)$

The result can be shown in multiple forms.

Point Form:

$(2, 5, - 1)$

Equation Form:

$x = 2, y = 5, z = - 1$

Solve the System of Equations 9x+3y-4z=37 4x+3y+7z=16 x-5y+8z=-31

Related Questions

Support LCMGCF.com by disabling your adblocker.