t^2 + k^2 = 9
2t^2 - 5k^2 = 6
Solve the simultaneous equations
Thanks
multiply 1st eqn by 5 ... 5t^2 + 5k^2 = 45
add eqns (to eliminate k) ... 7t^2 = 51
solve for t , substitute back to find k
should be two solutions for each unknown
To solve the given simultaneous equations:
First, let's rearrange the equations:
Equation 1: t^2 + k^2 = 9 -> Equation 1a: t^2 = 9 - k^2 -> Equation 1b: t = √(9 - k^2)
Equation 2: 2t^2 - 5k^2 = 6
Now, substitute Equation 1b into Equation 2:
2(√(9 - k^2))^2 - 5k^2 = 6
2(9 - k^2) - 5k^2 = 6
18 -2k^2 - 5k^2 = 6
-7k^2 = -12
k^2 = 12/7
k = ±√(12/7) or approximately ±1.392
Now, substitute these values back into Equation 1b to find the corresponding values of t:
For k = √(12/7):
t = √(9 - (√(12/7))^2) = √(9 - 12/7) = √(63/7 - 12/7) = √(51/7) = ±√(51/7) or approximately ±1.404
For k = -√(12/7):
t = √(9 - (-√(12/7))^2) = √(9 - 12/7) = √(63/7 - 12/7) = √(51/7) = ±√(51/7) or approximately ±1.404
So, the solutions to the simultaneous equations are:
(t, k) ≈ (1.404, 1.392), (-1.404, 1.392), (1.404, -1.392), (-1.404, -1.392)