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:

Do you know how to Solve the System of Equations (x-5)^2+(y-3)^2=90 x+y=2? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | seventy-six million three hundred ninety-six thousand thirty-eight |
---|

- 76396038 has 16 divisors, whose sum is
**156519216** - The reverse of 76396038 is
**83069367** - Previous prime number is
**41**

- Is Prime? no
- Number parity even
- Number length 8
- Sum of Digits 42
- Digital Root 6

Name | nine hundred sixty-two million five hundred forty-seven thousand eight hundred thirty-five |
---|

- 962547835 has 4 divisors, whose sum is
**1155057408** - The reverse of 962547835 is
**538745269** - Previous prime number is
**5**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 49
- Digital Root 4

Name | three hundred twenty-seven million five hundred thirty-seven thousand one hundred twenty-seven |
---|

- 327537127 has 4 divisors, whose sum is
**328047160** - The reverse of 327537127 is
**721735723** - Previous prime number is
**643**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 37
- Digital Root 1