Solve the System of Equations 3x+y+7z=9 9x-y+10z=-8 4x+y+7z=2

$3 x + y + 7 z = 9$ $9 x - y + 10 z = - 8$ $4 x + y + 7 z = 2$

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

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

$y + 7 z = 9 - 3 x$

$9 x - y + 10 z = - 8$

$4 x + y + 7 z = 2$

Subtract $7 z$ from both sides of the equation.

$y = 9 - 3 x - 7 z$

$9 x - y + 10 z = - 8$

$4 x + y + 7 z = 2$

$y = 9 - 3 x - 7 z$

$9 x - y + 10 z = - 8$

$4 x + y + 7 z = 2$

Replace all occurrences of $y$ with $9 - 3 x - 7 z$ in each equation.

Replace all occurrences of $y$ in $9 x - y + 10 z = - 8$ with $9 - 3 x - 7 z$ .

$9 x - (9 - 3 x - 7 z) + 10 z = - 8$

$y = 9 - 3 x - 7 z$

$4 x + y + 7 z = 2$

Simplify the left side.

Simplify $9 x - (9 - 3 x - 7 z) + 10 z$ .

Simplify each term.

Apply the distributive property.

$9 x - 1 \cdot 9 - (- 3 x) - (- 7 z) + 10 z = - 8$

$y = 9 - 3 x - 7 z$

$4 x + y + 7 z = 2$

Simplify.

Multiply $- 1$ by $9$ .

$9 x - 9 - (- 3 x) - (- 7 z) + 10 z = - 8$

$y = 9 - 3 x - 7 z$

$4 x + y + 7 z = 2$

Multiply $- 3$ by $- 1$ .

$9 x - 9 + 3 x - (- 7 z) + 10 z = - 8$

$y = 9 - 3 x - 7 z$

$4 x + y + 7 z = 2$

Multiply $- 7$ by $- 1$ .

$9 x - 9 + 3 x + 7 z + 10 z = - 8$

$y = 9 - 3 x - 7 z$

$4 x + y + 7 z = 2$

$9 x - 9 + 3 x + 7 z + 10 z = - 8$

$y = 9 - 3 x - 7 z$

$4 x + y + 7 z = 2$

$9 x - 9 + 3 x + 7 z + 10 z = - 8$

$y = 9 - 3 x - 7 z$

$4 x + y + 7 z = 2$

Simplify by adding terms.

Add $9 x$ and $3 x$ .

$12 x - 9 + 7 z + 10 z = - 8$

$y = 9 - 3 x - 7 z$

$4 x + y + 7 z = 2$

Add $7 z$ and $10 z$ .

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

$4 x + y + 7 z = 2$

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

$4 x + y + 7 z = 2$

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

$4 x + y + 7 z = 2$

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

$4 x + y + 7 z = 2$

Replace all occurrences of $y$ in $4 x + y + 7 z = 2$ with $9 - 3 x - 7 z$ .

$4 x + 9 - 3 x - 7 z + 7 z = 2$

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

Simplify the left side.

Simplify $4 x + 9 - 3 x - 7 z + 7 z$ .

Remove parentheses.

$4 x + 9 - 3 x - 7 z + 7 z = 2$

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

Combine the opposite terms in $4 x + 9 - 3 x - 7 z + 7 z$ .

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

$4 x + 9 - 3 x + 0 = 2$

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

Add $4 x + 9 - 3 x$ and $0$ .

$4 x + 9 - 3 x = 2$

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

$4 x + 9 - 3 x = 2$

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

Subtract $3 x$ from $4 x$ .

$x + 9 = 2$

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

$x + 9 = 2$

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

$x + 9 = 2$

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

$x + 9 = 2$

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

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

Subtract $9$ from both sides of the equation.

$x = 2 - 9$

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

Subtract $9$ from $2$ .

$x = - 7$

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

$x = - 7$

$12 x - 9 + 17 z = - 8$

$y = 9 - 3 x - 7 z$

Replace all occurrences of $x$ with $- 7$ in each equation.

Replace all occurrences of $x$ in $12 x - 9 + 17 z = - 8$ with $- 7$ .

$12 (- 7) - 9 + 17 z = - 8$

$x = - 7$

$y = 9 - 3 x - 7 z$

Simplify the left side.

Simplify $12 (- 7) - 9 + 17 z$ .

Multiply $12$ by $- 7$ .

$- 84 - 9 + 17 z = - 8$

$x = - 7$

$y = 9 - 3 x - 7 z$

Subtract $9$ from $- 84$ .

$- 93 + 17 z = - 8$

$x = - 7$

$y = 9 - 3 x - 7 z$

$- 93 + 17 z = - 8$

$x = - 7$

$y = 9 - 3 x - 7 z$

$- 93 + 17 z = - 8$

$x = - 7$

$y = 9 - 3 x - 7 z$

Replace all occurrences of $x$ in $y = 9 - 3 x - 7 z$ with $- 7$ .

$y = 9 - 3 \cdot - 7 - 7 z$

$- 93 + 17 z = - 8$

$x = - 7$

Simplify the right side.

Simplify $9 - 3 \cdot - 7 - 7 z$ .

Multiply $- 3$ by $- 7$ .

$y = 9 + 21 - 7 z$

$- 93 + 17 z = - 8$

$x = - 7$

Add $9$ and $21$ .

$y = 30 - 7 z$

$- 93 + 17 z = - 8$

$x = - 7$

$y = 30 - 7 z$

$- 93 + 17 z = - 8$

$x = - 7$

$y = 30 - 7 z$

$- 93 + 17 z = - 8$

$x = - 7$

$y = 30 - 7 z$

$- 93 + 17 z = - 8$

$x = - 7$

Solve for $z$ in $- 93 + 17 z = - 8$ .

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

Add $93$ to both sides of the equation.

$17 z = - 8 + 93$

$y = 30 - 7 z$

$x = - 7$

Add $- 8$ and $93$ .

$17 z = 85$

$y = 30 - 7 z$

$x = - 7$

$17 z = 85$

$y = 30 - 7 z$

$x = - 7$

Divide each term in $17 z = 85$ by $17$ and simplify.

Divide each term in $17 z = 85$ by $17$ .

$\frac{17 z}{17} = \frac{85}{17}$

$y = 30 - 7 z$

$x = - 7$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 z}{17} = \frac{85}{17}$

$y = 30 - 7 z$

$x = - 7$

Divide $z$ by $1$ .

$z = \frac{85}{17}$

$y = 30 - 7 z$

$x = - 7$

$z = \frac{85}{17}$

$y = 30 - 7 z$

$x = - 7$

$z = \frac{85}{17}$

$y = 30 - 7 z$

$x = - 7$

Simplify the right side.

Divide $85$ by $17$ .

$z = 5$

$y = 30 - 7 z$

$x = - 7$

$z = 5$

$y = 30 - 7 z$

$x = - 7$

$z = 5$

$y = 30 - 7 z$

$x = - 7$

$z = 5$

$y = 30 - 7 z$

$x = - 7$

Replace all occurrences of $z$ with $5$ in each equation.

Replace all occurrences of $z$ in $y = 30 - 7 z$ with $5$ .

$y = 30 - 7 \cdot 5$

$z = 5$

$x = - 7$

Simplify the right side.

Simplify $30 - 7 \cdot 5$ .

Multiply $- 7$ by $5$ .

$y = 30 - 35$

$z = 5$

$x = - 7$

Subtract $35$ from $30$ .

$y = - 5$

$z = 5$

$x = - 7$

$y = - 5$

$z = 5$

$x = - 7$

$y = - 5$

$z = 5$

$x = - 7$

$y = - 5$

$z = 5$

$x = - 7$

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

$(- 7, - 5, 5)$

The result can be shown in multiple forms.

Point Form:

$(- 7, - 5, 5)$

Equation Form:

$x = - 7, y = - 5, z = 5$

Solve the System of Equations 3x+y+7z=9 9x-y+10z=-8 4x+y+7z=2

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