Solve the System of Equations x-6y-2z=-8 -x+5y+3z=2 3x-2y-4z=18

$x - 6 y - 2 z = - 8$ $- x + 5 y + 3 z = 2$ $3 x - 2 y - 4 z = 18$

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

Add $6 y$ to both sides of the equation.

$x - 2 z = - 8 + 6 y$

$- x + 5 y + 3 z = 2$

$3 x - 2 y - 4 z = 18$

Add $2 z$ to both sides of the equation.

$x = - 8 + 6 y + 2 z$

$- x + 5 y + 3 z = 2$

$3 x - 2 y - 4 z = 18$

$x = - 8 + 6 y + 2 z$

$- x + 5 y + 3 z = 2$

$3 x - 2 y - 4 z = 18$

Replace all occurrences of $x$ with $- 8 + 6 y + 2 z$ in each equation.

Replace all occurrences of $x$ in $- x + 5 y + 3 z = 2$ with $- 8 + 6 y + 2 z$ .

$- (- 8 + 6 y + 2 z) + 5 y + 3 z = 2$

$x = - 8 + 6 y + 2 z$

$3 x - 2 y - 4 z = 18$

Simplify the left side.

Simplify $- (- 8 + 6 y + 2 z) + 5 y + 3 z$ .

Simplify each term.

Apply the distributive property.

$8 - (6 y) - (2 z) + 5 y + 3 z = 2$

$x = - 8 + 6 y + 2 z$

$3 x - 2 y - 4 z = 18$

Simplify.

Multiply $- 1$ by $- 8$ .

$8 - (6 y) - (2 z) + 5 y + 3 z = 2$

$x = - 8 + 6 y + 2 z$

$3 x - 2 y - 4 z = 18$

Multiply $6$ by $- 1$ .

$8 - 6 y - (2 z) + 5 y + 3 z = 2$

$x = - 8 + 6 y + 2 z$

$3 x - 2 y - 4 z = 18$

Multiply $2$ by $- 1$ .

$8 - 6 y - 2 z + 5 y + 3 z = 2$

$x = - 8 + 6 y + 2 z$

$3 x - 2 y - 4 z = 18$

$8 - 6 y - 2 z + 5 y + 3 z = 2$

$x = - 8 + 6 y + 2 z$

$3 x - 2 y - 4 z = 18$

$8 - 6 y - 2 z + 5 y + 3 z = 2$

$x = - 8 + 6 y + 2 z$

$3 x - 2 y - 4 z = 18$

Simplify by adding terms.

Add $- 6 y$ and $5 y$ .

$8 - y - 2 z + 3 z = 2$

$x = - 8 + 6 y + 2 z$

$3 x - 2 y - 4 z = 18$

Add $- 2 z$ and $3 z$ .

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

$3 x - 2 y - 4 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

$3 x - 2 y - 4 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

$3 x - 2 y - 4 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

$3 x - 2 y - 4 z = 18$

Replace all occurrences of $x$ in $3 x - 2 y - 4 z = 18$ with $- 8 + 6 y + 2 z$ .

$3 (- 8 + 6 y + 2 z) - 2 y - 4 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

Simplify the left side.

Simplify $3 (- 8 + 6 y + 2 z) - 2 y - 4 z$ .

Simplify each term.

Apply the distributive property.

$3 \cdot - 8 + 3 (6 y) + 3 (2 z) - 2 y - 4 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

Simplify.

Multiply $3$ by $- 8$ .

$- 24 + 3 (6 y) + 3 (2 z) - 2 y - 4 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

Multiply $6$ by $3$ .

$- 24 + 18 y + 3 (2 z) - 2 y - 4 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

Multiply $2$ by $3$ .

$- 24 + 18 y + 6 z - 2 y - 4 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

$- 24 + 18 y + 6 z - 2 y - 4 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

$- 24 + 18 y + 6 z - 2 y - 4 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

Simplify by adding terms.

Subtract $2 y$ from $18 y$ .

$- 24 + 16 y + 6 z - 4 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

Subtract $4 z$ from $6 z$ .

$- 24 + 16 y + 2 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

$- 24 + 16 y + 2 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

$- 24 + 16 y + 2 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

$- 24 + 16 y + 2 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

$- 24 + 16 y + 2 z = 18$

$8 - y + z = 2$

$x = - 8 + 6 y + 2 z$

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

Subtract $8$ from both sides of the equation.

$- y + z = 2 - 8$

$- 24 + 16 y + 2 z = 18$

$x = - 8 + 6 y + 2 z$

Add $y$ to both sides of the equation.

$z = 2 - 8 + y$

$- 24 + 16 y + 2 z = 18$

$x = - 8 + 6 y + 2 z$

Subtract $8$ from $2$ .

$z = - 6 + y$

$- 24 + 16 y + 2 z = 18$

$x = - 8 + 6 y + 2 z$

$z = - 6 + y$

$- 24 + 16 y + 2 z = 18$

$x = - 8 + 6 y + 2 z$

Replace all occurrences of $z$ with $- 6 + y$ in each equation.

Replace all occurrences of $z$ in $- 24 + 16 y + 2 z = 18$ with $- 6 + y$ .

$- 24 + 16 y + 2 (- 6 + y) = 18$

$z = - 6 + y$

$x = - 8 + 6 y + 2 z$

Simplify the left side.

Simplify $- 24 + 16 y + 2 (- 6 + y)$ .

Simplify each term.

Apply the distributive property.

$- 24 + 16 y + 2 \cdot - 6 + 2 y = 18$

$z = - 6 + y$

$x = - 8 + 6 y + 2 z$

Multiply $2$ by $- 6$ .

$- 24 + 16 y - 12 + 2 y = 18$

$z = - 6 + y$

$x = - 8 + 6 y + 2 z$

$- 24 + 16 y - 12 + 2 y = 18$

$z = - 6 + y$

$x = - 8 + 6 y + 2 z$

Simplify by adding terms.

Subtract $12$ from $- 24$ .

$16 y - 36 + 2 y = 18$

$z = - 6 + y$

$x = - 8 + 6 y + 2 z$

Add $16 y$ and $2 y$ .

$18 y - 36 = 18$

$z = - 6 + y$

$x = - 8 + 6 y + 2 z$

$18 y - 36 = 18$

$z = - 6 + y$

$x = - 8 + 6 y + 2 z$

$18 y - 36 = 18$

$z = - 6 + y$

$x = - 8 + 6 y + 2 z$

$18 y - 36 = 18$

$z = - 6 + y$

$x = - 8 + 6 y + 2 z$

Replace all occurrences of $z$ in $x = - 8 + 6 y + 2 z$ with $- 6 + y$ .

$x = - 8 + 6 y + 2 (- 6 + y)$

$18 y - 36 = 18$

$z = - 6 + y$

Simplify the right side.

Simplify $- 8 + 6 y + 2 (- 6 + y)$ .

Simplify each term.

Apply the distributive property.

$x = - 8 + 6 y + 2 \cdot - 6 + 2 y$

$18 y - 36 = 18$

$z = - 6 + y$

Multiply $2$ by $- 6$ .

$x = - 8 + 6 y - 12 + 2 y$

$18 y - 36 = 18$

$z = - 6 + y$

$x = - 8 + 6 y - 12 + 2 y$

$18 y - 36 = 18$

$z = - 6 + y$

Simplify by adding terms.

Subtract $12$ from $- 8$ .

$x = 6 y - 20 + 2 y$

$18 y - 36 = 18$

$z = - 6 + y$

Add $6 y$ and $2 y$ .

$x = 8 y - 20$

$18 y - 36 = 18$

$z = - 6 + y$

$x = 8 y - 20$

$18 y - 36 = 18$

$z = - 6 + y$

$x = 8 y - 20$

$18 y - 36 = 18$

$z = - 6 + y$

$x = 8 y - 20$

$18 y - 36 = 18$

$z = - 6 + y$

$x = 8 y - 20$

$18 y - 36 = 18$

$z = - 6 + y$

Solve for $y$ in $18 y - 36 = 18$ .

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

Add $36$ to both sides of the equation.

$18 y = 18 + 36$

$x = 8 y - 20$

$z = - 6 + y$

Add $18$ and $36$ .

$18 y = 54$

$x = 8 y - 20$

$z = - 6 + y$

$18 y = 54$

$x = 8 y - 20$

$z = - 6 + y$

Divide each term in $18 y = 54$ by $18$ and simplify.

Divide each term in $18 y = 54$ by $18$ .

$\frac{18 y}{18} = \frac{54}{18}$

$x = 8 y - 20$

$z = - 6 + y$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 y}{18} = \frac{54}{18}$

$x = 8 y - 20$

$z = - 6 + y$

Divide $y$ by $1$ .

$y = \frac{54}{18}$

$x = 8 y - 20$

$z = - 6 + y$

$y = \frac{54}{18}$

$x = 8 y - 20$

$z = - 6 + y$

$y = \frac{54}{18}$

$x = 8 y - 20$

$z = - 6 + y$

Simplify the right side.

Divide $54$ by $18$ .

$y = 3$

$x = 8 y - 20$

$z = - 6 + y$

$y = 3$

$x = 8 y - 20$

$z = - 6 + y$

$y = 3$

$x = 8 y - 20$

$z = - 6 + y$

$y = 3$

$x = 8 y - 20$

$z = - 6 + y$

Replace all occurrences of $y$ with $3$ in each equation.

Replace all occurrences of $y$ in $x = 8 y - 20$ with $3$ .

$x = 8 (3) - 20$

$y = 3$

$z = - 6 + y$

Simplify the right side.

Simplify $8 (3) - 20$ .

Multiply $8$ by $3$ .

$x = 24 - 20$

$y = 3$

$z = - 6 + y$

Subtract $20$ from $24$ .

$x = 4$

$y = 3$

$z = - 6 + y$

$x = 4$

$y = 3$

$z = - 6 + y$

$x = 4$

$y = 3$

$z = - 6 + y$

Replace all occurrences of $y$ in $z = - 6 + y$ with $3$ .

$z = - 6 + 3$

$x = 4$

$y = 3$

Simplify $z = - 6 + 3$ .

Simplify the left side.

Remove parentheses.

$z = - 6 + 3$

$x = 4$

$y = 3$

$z = - 6 + 3$

$x = 4$

$y = 3$

Simplify the right side.

Add $- 6$ and $3$ .

$z = - 3$

$x = 4$

$y = 3$

$z = - 3$

$x = 4$

$y = 3$

$z = - 3$

$x = 4$

$y = 3$

$z = - 3$

$x = 4$

$y = 3$

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

$(4, 3, - 3)$

The result can be shown in multiple forms.

Point Form:

$(4, 3, - 3)$

Equation Form:

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

Solve the System of Equations x-6y-2z=-8 -x+5y+3z=2 3x-2y-4z=18

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