Question

The given pair of linear equations 𝟖𝒙 + 𝒒𝒚 = 𝟏𝟒 and 𝒑𝒙 + 𝟒𝟐𝒚 = 𝟒𝟗 has infinitely many solutions, find the value of 𝒌 if 𝒑 − 𝒒 = 𝒌.

• A. $k=4$
• B. $k=7$
• C. $k=-12$
• D. $k=12$

Answer 1

Answer: (D)

Condition of infinitely many solution:

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Given:

𝟖𝒙 + 𝒒𝒚 = 𝟏𝟒 and 𝒑𝒙 + 𝟒𝟐𝒚 = 𝟒𝟗

So,

$\frac{8}{p}=\frac{q}{42}=\frac{14}{49}$

$\Rightarrow p=\frac{49\times 8}{14}$

$\Rightarrow p=28$

And, $q=\frac{42\times 14}{49}$

$\Rightarrow q=12$

Hence, $K=p-q$

$=28-12$

$k=16$