Algebra problem!!! Please help me!!!

Good morning Brainiac
x+y = 13
1/2 x +y = 10
We gonna solve x+y=13 for x
So let's start by adding -y to both sides
x+y -y = 13-y
x= -y +13
Now substitute -y+13 for x in 1/2 x +y=10
1/2 x +y = 10
1/2 (-y+13)+y=10
1/2 y + 13/2 = 10
Now add -13/2 to both sides
1/2 y+13/2 -13/2 = 10- 13/2
1/2 y = 7/2
Now eliminate the common denominator which is 2
y = 7
Now we have the value for y, so lets find the value for x by substitute 7 for y in x= -y+13
x= -y+13
x= -7 + 13
x= 6
Answer : (6,7)
The answer is B
I hope that's help and if you have questions please let me know :)
Good luck
[tex] \left \{ {{y=13} \atop {x=10}} \right. \sqrt[n]{x} \lim_{n \to \infty} a_n [/tex]{ x+y=13
1/2 x y = 10
A. (5,8)
B. (6,7)
C. (8,5)
D. (7,6)
look at the facts don't know but I think it is C. (8,5)