Replace all occurrences of <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> in <math><mstyle displaystyle="true"><mn>2</mn><mi>y</mi><mo>+</mo><mn>6</mn><mo>=</mo><mn>2</mn><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow></mstyle></math> with <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mn>2</mn><mrow><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mo>+</mo><mn>6</mn><mo>=</mo><mn>2</mn><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow></mstyle></math> .

Simplify the left side.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Simplify the right side.

Simplify <math><mstyle displaystyle="true"><mn>2</mn><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow></mstyle></math> .

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> from both sides of the equation.

Combine the opposite terms in <math><mstyle displaystyle="true"><mn>2</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>6</mn><mo>-</mo><mn>2</mn><mi>x</mi><mo>-</mo><mn>6</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>2</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>2</mn><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>2</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><mn>2</mn><mi>x</mi><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> .

If any individual factor on the left side of the equation is equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , the entire expression will be equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>1</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>x</mi><mo>-</mo><mn>1</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to both sides of the equation.

The final solution is all the values that make <math><mstyle displaystyle="true"><mn>2</mn><mi>x</mi><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> true.

Replace all occurrences of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> in <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> with <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Simplify the right side.

Raising <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> to any positive power yields <math><mstyle displaystyle="true"><mn>0</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><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> with <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

One to any power is one.

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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