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Question

For what values of a does the following systems of equations have solutions? Find those solutions.
x+ay=1,ax+y=2a

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Solution

Given equations,
x+ay=1(1)
ax+y=2a(2)
(1)×a(2)(a21)y=a
y=a1a2
For solution to be defined, 1a20
a±1
(1)x=1ay
=1a21a2=12a21a2
a=IR{1,1} , solution exists
Solution is x=12a21a2,y=a1a2

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