Replace all occurrences of <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> in <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>6</mn></mstyle></math> with <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi></mstyle></math> .

Simplify the left side.

Simplify <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>2</mn><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>4</mn><mi>x</mi></mstyle></math> from <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><mi>x</mi><mo>=</mo><mn>6</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> .

Replace all occurrences of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> in <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mn>2</mn><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> .

Simplify the right side.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> .

The solution to the system is the complete set of ordered pairs that are valid solutions.

The result can be shown in multiple forms.

Point Form:

Equation Form:

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