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

Replace all occurrences of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> in <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>5</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>90</mn></mstyle></math> with <math><mstyle displaystyle="true"><mn>2</mn><mo>-</mo><mi>y</mi></mstyle></math> .

Simplify the left side.

Simplify <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mrow><mo>(</mo><mn>2</mn><mo>-</mo><mi>y</mi><mo>)</mo></mrow><mo>-</mo><mn>5</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Simplify each term.

Subtract <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mo>-</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mrow><mo>(</mo><mo>-</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mrow><mo>(</mo><mo>-</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow></mstyle></math> .

Expand <math><mstyle displaystyle="true"><mrow><mo>(</mo><mo>-</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mrow><mo>(</mo><mo>-</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow></mstyle></math> using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

Multiply <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> by <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> by adding the exponents.

Move <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> by <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> .

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

Multiply <math><mstyle displaystyle="true"><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> .

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

Add <math><mstyle displaystyle="true"><mn>3</mn><mi>y</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>3</mn><mi>y</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow></mstyle></math> .

Expand <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow></mstyle></math> using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> by <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> .

Move <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> .

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

Subtract <math><mstyle displaystyle="true"><mn>3</mn><mi>y</mi></mstyle></math> from <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><mi>y</mi></mstyle></math> .

Simplify by adding terms.

Combine the opposite terms in <math><mstyle displaystyle="true"><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>6</mn><mi>y</mi><mo>+</mo><mn>9</mn><mo>+</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>6</mn><mi>y</mi><mo>+</mo><mn>9</mn></mstyle></math> .

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

Add <math><mstyle displaystyle="true"><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>9</mn><mo>+</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> and <math><mstyle displaystyle="true"><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> .

Move all terms not containing <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> to the right side of the equation.

Subtract <math><mstyle displaystyle="true"><mn>18</mn></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>18</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>90</mn></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mn>2</mn><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>72</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>2</mn><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>72</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mn>72</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

Simplify <math><mstyle displaystyle="true"><mo>±</mo><msqrt><mn>36</mn></msqrt></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>36</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>6</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the first solution.

Next, use the negative value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the second solution.

The complete solution is the result of both the positive and negative portions of the solution.

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><mo>-</mo><mi>y</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Simplify the right side.

Simplify <math><mstyle displaystyle="true"><mn>2</mn><mo>-</mo><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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><mo>-</mo><mi>y</mi></mstyle></math> with <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> .

Simplify the right side.

Simplify <math><mstyle displaystyle="true"><mn>2</mn><mo>-</mo><mrow><mo>(</mo><mo>-</mo><mn>6</mn><mo>)</mo></mrow></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>6</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>6</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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