Question

Given that these simultaneous equations
x-y=k
2x²+y²-15
have exactly one pair of solutions, find k.

The answer is supposedly (±3√10)/2, but I don't know how to get to the answer

Answer 1

The value of k is$(3\sqrt{ 10})/2$

How to solve the simultaneous equation?

Given:

x-y=k.............(eq i)

2x²+y²-15..............(eq ii)

We would make y the subject formula in eq ii

2x²+y²-15= 0

2x² + y²= 15

y²= 15-2x²

y= $\sqrt{15-2x^2}$...........(eq iii)

Substitute the value of y into eq i

x-($\sqrt{15-2x^2}$= k

x- ($\sqrt{15} - 2x$= k

k= $(3\sqrt{ 10})/2$

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