Question

a x + B Y is equal to 5 and b x + A Y is equal to 3 where A and B are constant​

Answer 1

Let,

ax+by=5 be equation 1 and

bx+ay=3 be equation 2.

Multiply a to the eqation 2 and b to equaiton 1. We get,

abx+b2y=5b

abx+a2y=3a

Now subract the equation. The x terms get cancelled.

b2−a2)y=5b−3a

y=5b−3ab2−a2

Similarly multiply a to equation 1 and b to equation 2 and subtract them.

y terms get cancel out.

a2x−aby=5a

b2a+aby=3b

We are left with,

(a2−b2)x=5a−3b

x=5a−3ba2−b2

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