x/2 + y/3 = 4; x/4 + y/6 = 2

(vi) x/2 + y/3 = 4; x/4 + y/6 = 2


Sol. x/2 + y/3 = 4
Multiplying the equation with 6, we get
3x + 2y = 24
Comparing with a1x + b1y = c1 we get, a1 = 3, b1 = 2, c1 = 24

x/4 + y/6 = 2
Multiplying the equation with 12, we get
3x + 2y = 24
Comparing with a2x + b2y = c2 we get, a2 = 3, b2 = 2, c2 = 24

a1/a2 = 3/3 = 1 ............ eq. no. (i)
b1/b2 = 3/3 = 1 ............ eq. no. (ii)
c1/c2 = 3/3 = 1 ............ eq. no. (iii)

From Equation (i) , (ii) and (iii) we get
a1/a2 = b1/b2 = c1/c2

∴ Infinitely Many Solutions.  

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