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

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

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

Add $y$ to both sides of the equation.

$x + 3 z = 3 + y$

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

$y - 5 z = - 3$

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

$x = 3 + y - 3 z$

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

$y - 5 z = - 3$

$x = 3 + y - 3 z$

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

$y - 5 z = - 3$

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

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

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

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Simplify.

Multiply $- 2$ by $3$ .

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

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Multiply $- 3$ by $- 2$ .

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

$x = 3 + y - 3 z$

$y - 5 z = - 3$

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

$x = 3 + y - 3 z$

$y - 5 z = - 3$

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

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Combine the opposite terms in $- 6 - 2 y + 6 z + 2 y - 6 z$ .

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

$- 6 + 6 z + 0 - 6 z = 6$

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Add $- 6 + 6 z$ and $0$ .

$- 6 + 6 z - 6 z = 6$

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Subtract $6 z$ from $6 z$ .

$- 6 + 0 = 6$

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Add $- 6$ and $0$ .

$- 6 = 6$

$x = 3 + y - 3 z$

$y - 5 z = - 3$

$- 6 = 6$

$x = 3 + y - 3 z$

$y - 5 z = - 3$

$- 6 = 6$

$x = 3 + y - 3 z$

$y - 5 z = - 3$

$- 6 = 6$

$x = 3 + y - 3 z$

$y - 5 z = - 3$

$- 6 = 6$

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Since $- 6 = 6$ is not true, there is no solution.

No solution

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

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