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Applications (Word Problem)

Solve: ax+b...

Question

Solve: $a x + b y = p$ , $b x - a y = q$ for $x$ only

A

\frac{a p - b q}{p^{2} - q^{2}}

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B

\frac{b p - a q}{a^{2} - b^{2}}

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C

\frac{a p + b q}{a^{2} + b^{2}}

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D

\frac{b p - a q}{p^{2} - q^{2}}

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Solution

The correct option is C $\frac{a p + b q}{a^{2} + b^{2}}$
The options are complex hence use of option method will not be convenient. Elimination method will be better here.
For finding value of $x$ , the terms of $y$ is to be eliminated by multiplying each question with exchange coefficient of $y$ i.e multiplying equation (i) by $a$ and (ii) by $b$
$a^{2} x + a b y = a p$
$b^{2} x - a b y = b q$
-------------------------------
$(a^{2} + b^{2}) x = a p + b q$ $\Rightarrow$ $x = \frac{a p + b q}{a^{2} + b^{2}}$

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