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Question

Solve the following pair of linear equation
ax+by=c
bx+ay=1+c

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Solution

Given equations are

ax+by=c

bx+ay=1+c

By cross multiplication, we get

xb(1+c)+ac=ya(1+c)+bc=1a2b2

xacbbc=ybc+aca=1a2b2

xc(ab)b=yc(ab)+a=1(a+b)(ab)

x=c(ab)b(a+b)(ab) and y=c(ab)+a(a+b)(ab)

x=ca+bb(a+b)(ab)=c(a+b)ba2b2

and y=ca+b+a(a+b)(ab)=ca+b+aa2+b2.

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