Question

solve the system of equations algebraically for x and y
{ x^2 + y^2 = 26
x + y = 6

a. (1,5) (1,4)
b. (4,5) (5,4)
c. (5,1) (5,1)
d. (1,5) (5,1)
e. no solution

Answer 1

Given : x^2+y^2=26
x+y=6
squaring on both sides
(x+y)^2=6^2
x^2+y^2+2xy=36
==>26+2xy=36
==>2xy=10
==>xy=5
==>x=5/y
now (5/y)^2+y^2=26
==>y^4-26y^2+25=0
on futher solving
x=1 or 5
y= 5 or 1