Maths-
General
Easy

Question

In the system of equation below, a and c are constant
1 half straight x space plus space 1 third straight y space equals space 1 over 6
ax space plus space straight y space equals space 6
If the system of equation has an infinite number of solutions (x , y), what is the value of a ?

  1. negative 1 half
  2. 0
  3. 1 half
  4. 3 over 2

The correct answer is: 3 over 2


    HINT :- if two equation ax + by = c and px + qy = r have infinite no. of solutions then we get  straight a over straight p equals straight b over straight q equals straight c over straight r.
    Here the given equations are 1 half x space plus space 1 third y space equals space 1 over 6  and ax space plus space straight y space equals space straight c where a and c are constants
    Now applying condition as they have infinite roots
    fraction numerator begin display style 1 half end style over denominator straight a end fraction space equals space fraction numerator begin display style 1 third end style over denominator 1 end fraction space equals space fraction numerator begin display style 1 over 6 end style over denominator straight c end fraction
    From fraction numerator begin display style 1 half end style over denominator a end fraction space equals space fraction numerator begin display style 1 third end style over denominator 1 end fraction not stretchy rightwards double arrow space a space equals space fraction numerator begin display style 1 half end style over denominator begin display style 1 third end style end fraction equals space 3 over 2
    ∴a = 3 over 2

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