Answer:
24
Step-by-step explanation:
We have a system of equations, so we can start with the second equation:
[tex]x-y=2[/tex]
And move y to the other side to isolate x:
[tex]x=2+y[/tex]
Now we can replace x into the first equation:
[tex](2+y)^{2} -y^{2} =48\\ (2+y)(2+y)-y^{2} =48\\ 4+4y+y^{2} -y^{2} =48[/tex]
Notice that we can cancel out the y squared terms:
[tex]4+4y=48\\ 4y=44\\ y=11[/tex]
Now we just need to find x by replacing y into the second equation:
[tex]x-11=2\\ x=13[/tex]
And finally, add them:
[tex]x+y=11+13\\ x+y=24[/tex]
Hope this helps.
Answer:
x= 13
y=11
x^2 - y^2 = 48 and x - y = 2
x = 2 + y
(2 + y)^2 - y^2 = 48
(2 + y) (2 + y) - y^2 = 4
(4 + 2y +2y + y^2) -y^2 = 48
4 + 4y + y^2 - y^2 = 48
4 + 4y = 48
4y = 48 -4
4y = 44
y= 44/4
y= 11
Plug y back into the original equation:
x^2 - y^2 = 48
x^2 - 11^2 = 48
x^2 - 121 = 48
x^2 = 121 + 48
x^2 = 169
The square root of 169 is 13
So x= 13
x + y
13 + 11 = 24
