Add <math><mstyle displaystyle="true"><mn>4</mn><mi>y</mi></mstyle></math> to both sides of the equation.

Replace all occurrences of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> in <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi><mo>+</mo><mn>4</mn><mi>y</mi><mo>-</mo><mn>8</mn><mo>=</mo><mn>0</mn></mstyle></math> with <math><mstyle displaystyle="true"><mo>-</mo><mn>8</mn><mo>+</mo><mn>4</mn><mi>y</mi></mstyle></math> .

Simplify the left side.

Simplify <math><mstyle displaystyle="true"><mo>-</mo><mrow><mo>(</mo><mo>-</mo><mn>8</mn><mo>+</mo><mn>4</mn><mi>y</mi><mo>)</mo></mrow><mo>+</mo><mn>4</mn><mi>y</mi><mo>-</mo><mn>8</mn></mstyle></math> .

Simplify each term.

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>8</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Combine the opposite terms in <math><mstyle displaystyle="true"><mn>8</mn><mo>-</mo><mn>4</mn><mi>y</mi><mo>+</mo><mn>4</mn><mi>y</mi><mo>-</mo><mn>8</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mi>y</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn><mi>y</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

Remove any equations from the system that are always true.

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