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

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

Step 1

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

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

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

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

$2 x + 4 y - 2 z = - 4$

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

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

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

$2 x + 4 y - 2 z = - 4$

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

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

$2 x + 4 y - 2 z = - 4$

Step 2

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

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

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

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

$2 x + 4 y - 2 z = - 4$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

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

$2 x + 4 y - 2 z = - 4$

Simplify.

Multiply $2$ by $- 2$ .

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

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

$2 x + 4 y - 2 z = - 4$

Multiply $- 2$ by $2$ .

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

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

$2 x + 4 y - 2 z = - 4$

Multiply $2$ by $2$ .

$- 4 - 4 y + 4 z + 4 y - 6 z = 8$

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

$2 x + 4 y - 2 z = - 4$

$- 4 - 4 y + 4 z + 4 y - 6 z = 8$

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

$2 x + 4 y - 2 z = - 4$

$- 4 - 4 y + 4 z + 4 y - 6 z = 8$

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

$2 x + 4 y - 2 z = - 4$

Simplify by adding terms.

Combine the opposite terms in $- 4 - 4 y + 4 z + 4 y - 6 z$ .

Add $- 4 y$ and $4 y$ .

$- 4 + 4 z + 0 - 6 z = 8$

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

$2 x + 4 y - 2 z = - 4$

Add $- 4 + 4 z$ and $0$ .

$- 4 + 4 z - 6 z = 8$

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

$2 x + 4 y - 2 z = - 4$

$- 4 + 4 z - 6 z = 8$

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

$2 x + 4 y - 2 z = - 4$

Subtract $6 z$ from $4 z$ .

$- 4 - 2 z = 8$

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

$2 x + 4 y - 2 z = - 4$

$- 4 - 2 z = 8$

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

$2 x + 4 y - 2 z = - 4$

$- 4 - 2 z = 8$

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

$2 x + 4 y - 2 z = - 4$

$- 4 - 2 z = 8$

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

$2 x + 4 y - 2 z = - 4$

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

$2 (- 2 - 2 y + 2 z) + 4 y - 2 z = - 4$

$- 4 - 2 z = 8$

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

Simplify the left side.

Simplify $2 (- 2 - 2 y + 2 z) + 4 y - 2 z$ .

Simplify each term.

Apply the distributive property.

$2 \cdot - 2 + 2 (- 2 y) + 2 (2 z) + 4 y - 2 z = - 4$

$- 4 - 2 z = 8$

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

Simplify.

Multiply $2$ by $- 2$ .

$- 4 + 2 (- 2 y) + 2 (2 z) + 4 y - 2 z = - 4$

$- 4 - 2 z = 8$

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

Multiply $- 2$ by $2$ .

$- 4 - 4 y + 2 (2 z) + 4 y - 2 z = - 4$

$- 4 - 2 z = 8$

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

Multiply $2$ by $2$ .

$- 4 - 4 y + 4 z + 4 y - 2 z = - 4$

$- 4 - 2 z = 8$

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

$- 4 - 4 y + 4 z + 4 y - 2 z = - 4$

$- 4 - 2 z = 8$

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

$- 4 - 4 y + 4 z + 4 y - 2 z = - 4$

$- 4 - 2 z = 8$

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

Simplify by adding terms.

Combine the opposite terms in $- 4 - 4 y + 4 z + 4 y - 2 z$ .

Add $- 4 y$ and $4 y$ .

$- 4 + 4 z + 0 - 2 z = - 4$

$- 4 - 2 z = 8$

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

Add $- 4 + 4 z$ and $0$ .

$- 4 + 4 z - 2 z = - 4$

$- 4 - 2 z = 8$

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

$- 4 + 4 z - 2 z = - 4$

$- 4 - 2 z = 8$

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

Subtract $2 z$ from $4 z$ .

$- 4 + 2 z = - 4$

$- 4 - 2 z = 8$

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

$- 4 + 2 z = - 4$

$- 4 - 2 z = 8$

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

$- 4 + 2 z = - 4$

$- 4 - 2 z = 8$

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

$- 4 + 2 z = - 4$

$- 4 - 2 z = 8$

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

$- 4 + 2 z = - 4$

$- 4 - 2 z = 8$

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

Step 3

Solve for $z$ in $- 4 + 2 z = - 4$ .

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

Add $4$ to both sides of the equation.

$2 z = - 4 + 4$

$- 4 - 2 z = 8$

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

Add $- 4$ and $4$ .

$2 z = 0$

$- 4 - 2 z = 8$

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

$2 z = 0$

$- 4 - 2 z = 8$

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

Divide each term in $2 z = 0$ by $2$ and simplify.

Divide each term in $2 z = 0$ by $2$ .

$\frac{2 z}{2} = \frac{0}{2}$

$- 4 - 2 z = 8$

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 z}{2} = \frac{0}{2}$

$- 4 - 2 z = 8$

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

Divide $z$ by $1$ .

$z = \frac{0}{2}$

$- 4 - 2 z = 8$

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

$z = \frac{0}{2}$

$- 4 - 2 z = 8$

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

$z = \frac{0}{2}$

$- 4 - 2 z = 8$

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

Simplify the right side.

Divide $0$ by $2$ .

$z = 0$

$- 4 - 2 z = 8$

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

$z = 0$

$- 4 - 2 z = 8$

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

$z = 0$

$- 4 - 2 z = 8$

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

$z = 0$

$- 4 - 2 z = 8$

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

Step 4

Replace all occurrences of $z$ with $0$ in each equation.

Replace all occurrences of $z$ in $- 4 - 2 z = 8$ with $0$ .

$- 4 - 2 \cdot 0 = 8$

$z = 0$

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

Simplify the left side.

Simplify $- 4 - 2 \cdot 0$ .

Multiply $- 2$ by $0$ .

$- 4 + 0 = 8$

$z = 0$

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

Add $- 4$ and $0$ .

$- 4 = 8$

$z = 0$

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

$- 4 = 8$

$z = 0$

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

$- 4 = 8$

$z = 0$

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

Replace all occurrences of $z$ in $x = - 2 - 2 y + 2 z$ with $0$ .

$x = - 2 - 2 y + 2 (0)$

$- 4 = 8$

$z = 0$

Simplify the right side.

Simplify $- 2 - 2 y + 2 (0)$ .

Multiply $2$ by $0$ .

$x = - 2 - 2 y + 0$

$- 4 = 8$

$z = 0$

Add $- 2 - 2 y$ and $0$ .

$x = - 2 - 2 y$

$- 4 = 8$

$z = 0$

$x = - 2 - 2 y$

$- 4 = 8$

$z = 0$

$x = - 2 - 2 y$

$- 4 = 8$

$z = 0$

$x = - 2 - 2 y$

$- 4 = 8$

$z = 0$

Step 5

Since $- 4 = 8$ is not true, there is no solution.

No solution

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

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