Answer:
20
Step-by-step explanation:
Let's start by rewriting the second equation in terms of "x":
[tex]x+y=5[/tex]
Subtract y from both sides:
[tex]x=5-y[/tex]
Now, substitute "5-y" for "x" in the first equation:
[tex](5-y)^2-y^2=100[/tex]
Note that:
[tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex]25-10y+y^2-y^2=100[/tex]
Cancel out like terms:
[tex]25-10y=100[/tex]
Subtract 25 from both sides:
[tex]-10y=75[/tex]
Divide both sides by -10
[tex]y=\frac{75}{-10}=\frac{15}{-2}=-\frac{15}{2}[/tex]
Now, substitute this value back into either of the equations to solve for x.
[tex]x+y=5\\x-\frac{15}{2}=5\\[/tex]
Add 15/2 to both sides:
[tex]x=5+\frac{15}{2}\\x=\frac{10}{2}+\frac{15}{2}\\x=\frac{25}{2}[/tex]
Now, find the difference:
[tex]x-y=\frac{25}{2}-(-\frac{15}{2})=\frac{25}{2}+\frac{15}{2}=\frac{40}{2}=20[/tex]
