Easy

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

$(8,4)$

$(4,8)$

$(3,6)$

$(6,3)$

✅ Correct Option: 2

For infinite solutions, the equations must be proportional. Given equations: $2x + 3y = 7$ ...(1) $2px + (p+q)y = 28$ ...(2) For infinite solutions, coefficients must be proportional: $\frac{2}{2p} = \frac{3}{p+q} = \frac{7}{28}$ From $\frac{7}{28} = \frac{1}{4}$: $\frac{2}{2p} = \frac{1}{4}$ $p = 4$ And $\frac{3}{p+q} = \frac{1}{4}$ $\frac{3}{4+q} = \frac{1}{4}$ $3 = 4+q$ $q = 8$ Therefore $(p,q) = (4,8)$

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

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