Algebra Examples

$x + 8 = y - 1$ $z + 13 = x + 16$ $y - 12 = z - 6$

Step 1

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

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Step 1.1

Subtract $8$ from both sides of the equation.

$x = y - 1 - 8$

$z + 13 = x + 16$

$y - 12 = z - 6$

Step 1.2

Subtract $8$ from $- 1$ .

$x = y - 9$

$z + 13 = x + 16$

$y - 12 = z - 6$

$x = y - 9$

$z + 13 = x + 16$

$y - 12 = z - 6$

Step 2

Replace all occurrences of $x$ with $y - 9$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $z + 13 = x + 16$ with $y - 9$ .

$z + 13 = (y - 9) + 16$

$x = y - 9$

$y - 12 = z - 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Add $- 9$ and $16$ .

$z + 13 = y + 7$

$x = y - 9$

$y - 12 = z - 6$

$z + 13 = y + 7$

$x = y - 9$

$y - 12 = z - 6$

$z + 13 = y + 7$

$x = y - 9$

$y - 12 = z - 6$

Step 3

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

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Step 3.1

Subtract $13$ from both sides of the equation.

$z = y + 7 - 13$

$x = y - 9$

$y - 12 = z - 6$

Step 3.2

Subtract $13$ from $7$ .

$z = y - 6$

$x = y - 9$

$y - 12 = z - 6$

$z = y - 6$

$x = y - 9$

$y - 12 = z - 6$

Step 4

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

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Step 4.1

Replace all occurrences of $z$ in $y - 12 = z - 6$ with $y - 6$ .

$y - 12 = (y - 6) - 6$

$z = y - 6$

$x = y - 9$

Step 4.2

Simplify the right side.

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Step 4.2.1

Subtract $6$ from $- 6$ .

$y - 12 = y - 12$

$z = y - 6$

$x = y - 9$

$y - 12 = y - 12$

$z = y - 6$

$x = y - 9$

$y - 12 = y - 12$

$z = y - 6$

$x = y - 9$

Step 5

Remove any equations from the system that are always true.

$z = y - 6$

$x = y - 9$