Solve the System of Equations x^2+y^2=25 y=3/4x-25/4

Rewrite ${\displaystyle {(\frac{3x}{4}-\frac{25}{4})}^2}$ as ${\displaystyle (\frac{3x}{4}-\frac{25}{4})(\frac{3x}{4}-\frac{25}{4})}$.

Expand ${\displaystyle (\frac{3x}{4}-\frac{25}{4})(\frac{3x}{4}-\frac{25}{4})}$ using the FOIL Method.

Simplify and combine like terms.

Simplify each term.

Combine ${\displaystyle x^2}$ and ${\displaystyle \frac{16}{16}}$.

Combine the numerators over the common denominator.

Combine the numerators over the common denominator.

Factor ${\displaystyle 25}$ out of ${\displaystyle 25x^2+625}$.

Move the negative in front of the fraction.

Multiply ${\displaystyle \frac{75x}{8}}$ by ${\displaystyle \frac{2}{2}}$.

Multiply ${\displaystyle 8}$ by ${\displaystyle 2}$.

Factor ${\displaystyle 25}$ out of ${\displaystyle 25(x^2+25)-75x\cdot 2}$.

Multiply ${\displaystyle 2}$ by ${\displaystyle -3}$.

Reorder terms.

Cancel the common factor of ${\displaystyle 16}$.

Apply the distributive property.

Simplify.

Factor ${\displaystyle 25}$ out of ${\displaystyle 25x^2}$.

Factor ${\displaystyle 25}$ out of ${\displaystyle -150x}$.

Factor ${\displaystyle 25}$ out of ${\displaystyle 225}$.

Factor ${\displaystyle 25}$ out of ${\displaystyle 25x^2+25(-6x)}$.

Factor ${\displaystyle 25}$ out of ${\displaystyle 25(x^2-6x)+25\cdot 9}$.

Rewrite ${\displaystyle 9}$ as ${\displaystyle 3^2}$.

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

Rewrite the polynomial.

Factor using the perfect square trinomial rule ${\displaystyle a^2-2ab+b^2={(a-b)}^2}$, where ${\displaystyle a=x}$ and ${\displaystyle b=3}$.

Cancel the common factor of ${\displaystyle 25}$.

Divide ${\displaystyle 0}$ by ${\displaystyle 25}$.

Multiply ${\displaystyle 3}$ by ${\displaystyle 3}$.

Subtract ${\displaystyle 25}$ from ${\displaystyle 9}$.

Divide ${\displaystyle -16}$ by ${\displaystyle 4}$.