Algebra Examples

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

Step 1

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

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Step 1.1

Add $y$ to both sides of the equation.

$x + 3 z = 3 + y$

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

$y - 5 z = - 3$

Step 1.2

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

$x = 3 + y - 3 z$

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

$y - 5 z = - 3$

$x = 3 + y - 3 z$

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

$y - 5 z = - 3$

Step 2

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

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Step 2.1

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

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

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

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

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Step 2.2.1.1.2

Simplify.

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Step 2.2.1.1.2.1

Multiply $- 2$ by $3$ .

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

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Step 2.2.1.1.2.2

Multiply $- 3$ by $- 2$ .

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

$x = 3 + y - 3 z$

$y - 5 z = - 3$

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

$x = 3 + y - 3 z$

$y - 5 z = - 3$

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

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Step 2.2.1.2

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

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Step 2.2.1.2.1

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

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

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Step 2.2.1.2.2

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

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

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Step 2.2.1.2.3

Subtract $6 z$ from $6 z$ .

$- 6 + 0 = 6$

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Step 2.2.1.2.4

Add $- 6$ and $0$ .

$- 6 = 6$

$x = 3 + y - 3 z$

$y - 5 z = - 3$

$- 6 = 6$

$x = 3 + y - 3 z$

$y - 5 z = - 3$

$- 6 = 6$

$x = 3 + y - 3 z$

$y - 5 z = - 3$

$- 6 = 6$

$x = 3 + y - 3 z$

$y - 5 z = - 3$

$- 6 = 6$

$x = 3 + y - 3 z$

$y - 5 z = - 3$

Step 3

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

No solution