Question 21

If the pair of linear equations $$2x + 3y = 7$$ and $$2px + (p + q)y = 28$$ has an infinite number of solutions, then $$(p, q)$$:

Solution

For pair of linear equations : $$a_1x+b_1y=c_1\ \&\ a_2x+b_2y=c_2$$ to have an infinite no of solutions , the below given condition has to hold true .
$$\dfrac{a_1\ }{a_2}=\dfrac{\ b_1}{b_2}=\dfrac{\ c_1}{c_2}$$

So, it implies : $$\dfrac{2 }{2p}=\dfrac{3}{p+q}=\dfrac{7}{28}$$

Therefore, P = 4, Q = 8.

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