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The value of k is[tex](3\sqrt{ 10})/2[/tex]
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= [tex]\sqrt{15-2x^2}[/tex]...........(eq iii)
Substitute the value of y into eq i
x-([tex]\sqrt{15-2x^2}[/tex]= k
x- ([tex]\sqrt{15} - 2x[/tex]= k
k= [tex](3\sqrt{ 10})/2[/tex]
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