Question

How do you solve the system x^2 + y^2 = 2500 and y^2/60^2 + x^2/40^2 = 1 without graphing?

Answer 1

There may be several ways to solve this without graphing. One method is to take the second equation and perform the addition using the common denominator of (40^2)*(60^2) resulting in 40^2 y^2 + 60^2 x^2 = 40^2*60^2 Divide this thru by 40^2 getting
\[y ^{2} + 2.25x ^{2}=3600\]Now subtract the first equation of problem from this equation (eliminating y^2) getting:\[1.25x ^{2}=1100\]Solve for x as x=sqrt 880 or approx 29.66

Answer 2

Now solve for y^2 by subtracting x^2 (880) from 2500 provided in first equation. Getting y^2= 1620 Solve for y
Verify by checking via substitution.