Solve by Substitution x^2+y^2=25 , x-y=1

Simplify each term.

Add ${\displaystyle y^2}$ and ${\displaystyle y^2}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle 2y}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle 2y^2}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle -24}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle 2\left(y\right)+2y^2}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle 2(y+y^2)+2\cdot -12}$.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle -12}$ and whose sum is ${\displaystyle 1}$.

Write the factored form using these integers.

Replace all occurrences of ${\displaystyle u}$ with ${\displaystyle y}$.

Remove unnecessary parentheses.

Remove parentheses.

Add ${\displaystyle 1}$ and ${\displaystyle 3}$.

Remove parentheses.

Subtract ${\displaystyle 4}$ from ${\displaystyle 1}$.