Question

solved that...
ax+by=c
bx+ay=1+c

Answer 1

Sol :
Given equations are ax+by = c --------------(1) and ay+bx = c+1 --------------(2)
multiply equation (1) by 'b' and equation (2) by 'a' we get
abx+b2y = bc
abx +a2y= ac+a (substract)
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( b2-a2)y = bc - ac -a
y = (bc - ac -a) / ( b2-a2)
multiply equation (1) by 'a' and equation (2) by 'b' we get
a2x+aby = ac
aby+b2x = bc+b (substract)
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(a2- b2)x = (ac-bc -b)
x = (ac-bc -b) / (a2- b2)
∴ the values of x and y are (ac-bc -b) / (a2- b2) , (bc - ac -a) / ( b2-a2)

Answer 2

first add the equations
ax+by+bx+ay=c+1+c
x(a+b)+y(a+b)=1+2c
(a+b)(x+y)=1+2c
x+y=1+2c/(a+b)
now subtract
ax-bx+by-ay=c-1+c
x(a-b)+y(a-b)=1
x+y=1/(a-b)


now solve