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

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

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

Subtract $2 x$ from both sides of the equation.

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

$6 x - 5 y - z = - 2$

$4 x + 4 y + z = - 8$

Subtract $6 y$ from both sides of the equation.

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

$6 x - 5 y - z = - 2$

$4 x + 4 y + z = - 8$

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

$6 x - 5 y - z = - 2$

$4 x + 4 y + z = - 8$

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

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

$6 x - 5 y - (- 6 - 2 x - 6 y) = - 2$

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

$4 x + 4 y + z = - 8$

Simplify the left side.

Simplify $6 x - 5 y - (- 6 - 2 x - 6 y)$ .

Simplify each term.

Apply the distributive property.

$6 x - 5 y + 6 - (- 2 x) - (- 6 y) = - 2$

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

$4 x + 4 y + z = - 8$

Simplify.

Multiply $- 1$ by $- 6$ .

$6 x - 5 y + 6 - (- 2 x) - (- 6 y) = - 2$

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

$4 x + 4 y + z = - 8$

Multiply $- 2$ by $- 1$ .

$6 x - 5 y + 6 + 2 x - (- 6 y) = - 2$

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

$4 x + 4 y + z = - 8$

Multiply $- 6$ by $- 1$ .

$6 x - 5 y + 6 + 2 x + 6 y = - 2$

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

$4 x + 4 y + z = - 8$

$6 x - 5 y + 6 + 2 x + 6 y = - 2$

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

$4 x + 4 y + z = - 8$

$6 x - 5 y + 6 + 2 x + 6 y = - 2$

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

$4 x + 4 y + z = - 8$

Simplify by adding terms.

Add $6 x$ and $2 x$ .

$8 x - 5 y + 6 + 6 y = - 2$

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

$4 x + 4 y + z = - 8$

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

$8 x + y + 6 = - 2$

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

$4 x + 4 y + z = - 8$

$8 x + y + 6 = - 2$

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

$4 x + 4 y + z = - 8$

$8 x + y + 6 = - 2$

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

$4 x + 4 y + z = - 8$

$8 x + y + 6 = - 2$

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

$4 x + 4 y + z = - 8$

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

$4 x + 4 y - 6 - 2 x - 6 y = - 8$

$8 x + y + 6 = - 2$

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

Simplify the left side.

Simplify $4 x + 4 y - 6 - 2 x - 6 y$ .

Remove parentheses.

$4 x + 4 y - 6 - 2 x - 6 y = - 8$

$8 x + y + 6 = - 2$

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

Subtract $2 x$ from $4 x$ .

$2 x + 4 y - 6 - 6 y = - 8$

$8 x + y + 6 = - 2$

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

Subtract $6 y$ from $4 y$ .

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

$8 x + y + 6 = - 2$

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

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

$8 x + y + 6 = - 2$

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

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

$8 x + y + 6 = - 2$

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

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

$8 x + y + 6 = - 2$

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

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

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

$y + 6 = - 2 - 8 x$

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

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

Subtract $6$ from both sides of the equation.

$y = - 2 - 8 x - 6$

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

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

Subtract $6$ from $- 2$ .

$y = - 8 x - 8$

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

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

$y = - 8 x - 8$

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

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

Replace all occurrences of $y$ with $- 8 x - 8$ in each equation.

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

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

$y = - 8 x - 8$

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

Simplify the left side.

Simplify $2 x - 2 (- 8 x - 8) - 6$ .

Simplify each term.

Apply the distributive property.

$2 x - 2 (- 8 x) - 2 \cdot - 8 - 6 = - 8$

$y = - 8 x - 8$

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

Multiply $- 8$ by $- 2$ .

$2 x + 16 x - 2 \cdot - 8 - 6 = - 8$

$y = - 8 x - 8$

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

Multiply $- 2$ by $- 8$ .

$2 x + 16 x + 16 - 6 = - 8$

$y = - 8 x - 8$

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

$2 x + 16 x + 16 - 6 = - 8$

$y = - 8 x - 8$

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

Simplify by adding terms.

Add $2 x$ and $16 x$ .

$18 x + 16 - 6 = - 8$

$y = - 8 x - 8$

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

Subtract $6$ from $16$ .

$18 x + 10 = - 8$

$y = - 8 x - 8$

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

$18 x + 10 = - 8$

$y = - 8 x - 8$

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

$18 x + 10 = - 8$

$y = - 8 x - 8$

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

$18 x + 10 = - 8$

$y = - 8 x - 8$

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

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

$z = - 6 - 2 x - 6 (- 8 x - 8)$

$18 x + 10 = - 8$

$y = - 8 x - 8$

Simplify the right side.

Simplify $- 6 - 2 x - 6 (- 8 x - 8)$ .

Simplify each term.

Apply the distributive property.

$z = - 6 - 2 x - 6 (- 8 x) - 6 \cdot - 8$

$18 x + 10 = - 8$

$y = - 8 x - 8$

Multiply $- 8$ by $- 6$ .

$z = - 6 - 2 x + 48 x - 6 \cdot - 8$

$18 x + 10 = - 8$

$y = - 8 x - 8$

Multiply $- 6$ by $- 8$ .

$z = - 6 - 2 x + 48 x + 48$

$18 x + 10 = - 8$

$y = - 8 x - 8$

$z = - 6 - 2 x + 48 x + 48$

$18 x + 10 = - 8$

$y = - 8 x - 8$

Simplify by adding terms.

Add $- 6$ and $48$ .

$z = - 2 x + 48 x + 42$

$18 x + 10 = - 8$

$y = - 8 x - 8$

Add $- 2 x$ and $48 x$ .

$z = 46 x + 42$

$18 x + 10 = - 8$

$y = - 8 x - 8$

$z = 46 x + 42$

$18 x + 10 = - 8$

$y = - 8 x - 8$

$z = 46 x + 42$

$18 x + 10 = - 8$

$y = - 8 x - 8$

$z = 46 x + 42$

$18 x + 10 = - 8$

$y = - 8 x - 8$

$z = 46 x + 42$

$18 x + 10 = - 8$

$y = - 8 x - 8$

Solve for $x$ in $18 x + 10 = - 8$ .

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

Subtract $10$ from both sides of the equation.

$18 x = - 8 - 10$

$z = 46 x + 42$

$y = - 8 x - 8$

Subtract $10$ from $- 8$ .

$18 x = - 18$

$z = 46 x + 42$

$y = - 8 x - 8$

$18 x = - 18$

$z = 46 x + 42$

$y = - 8 x - 8$

Divide each term in $18 x = - 18$ by $18$ and simplify.

Divide each term in $18 x = - 18$ by $18$ .

$\frac{18 x}{18} = \frac{- 18}{18}$

$z = 46 x + 42$

$y = - 8 x - 8$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 x}{18} = \frac{- 18}{18}$

$z = 46 x + 42$

$y = - 8 x - 8$

Divide $x$ by $1$ .

$x = \frac{- 18}{18}$

$z = 46 x + 42$

$y = - 8 x - 8$

$x = \frac{- 18}{18}$

$z = 46 x + 42$

$y = - 8 x - 8$

$x = \frac{- 18}{18}$

$z = 46 x + 42$

$y = - 8 x - 8$

Simplify the right side.

Divide $- 18$ by $18$ .

$x = - 1$

$z = 46 x + 42$

$y = - 8 x - 8$

$x = - 1$

$z = 46 x + 42$

$y = - 8 x - 8$

$x = - 1$

$z = 46 x + 42$

$y = - 8 x - 8$

$x = - 1$

$z = 46 x + 42$

$y = - 8 x - 8$

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

Replace all occurrences of $x$ in $z = 46 x + 42$ with $- 1$ .

$z = 46 (- 1) + 42$

$x = - 1$

$y = - 8 x - 8$

Simplify the right side.

Simplify $46 (- 1) + 42$ .

Multiply $46$ by $- 1$ .

$z = - 46 + 42$

$x = - 1$

$y = - 8 x - 8$

Add $- 46$ and $42$ .

$z = - 4$

$x = - 1$

$y = - 8 x - 8$

$z = - 4$

$x = - 1$

$y = - 8 x - 8$

$z = - 4$

$x = - 1$

$y = - 8 x - 8$

Replace all occurrences of $x$ in $y = - 8 x - 8$ with $- 1$ .

$y = - 8 \cdot - 1 - 8$

$z = - 4$

$x = - 1$

Simplify the right side.

Simplify $- 8 \cdot - 1 - 8$ .

Multiply $- 8$ by $- 1$ .

$y = 8 - 8$

$z = - 4$

$x = - 1$

Subtract $8$ from $8$ .

$y = 0$

$z = - 4$

$x = - 1$

$y = 0$

$z = - 4$

$x = - 1$

$y = 0$

$z = - 4$

$x = - 1$

$y = 0$

$z = - 4$

$x = - 1$

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

$(- 1, 0, - 4)$

The result can be shown in multiple forms.

Point Form:

$(- 1, 0, - 4)$

Equation Form:

$x = - 1, y = 0, z = - 4$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.