Explain method of elimination by equation coefficients.

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Solution

In elimination method, the coefficients of the given equations are multiplied by any constant to make coefficient of $1$ variable same is both equation. And other value can be find out.
Let $a x + b y = c$ ……….. $(1)$
$p x + q y = r$ ………….. $(2)$
Multiply equation $(1)$ by P & $(2)$ by a we get
$a p x + b p y = c p$ ………… $(3)$
$a p x + a q y = a r$ ………….. $(4)$
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$y [b p - a q] = c p - a r$
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$[y = \frac{c p - a r}{b p - a q}]$ and $x = \frac{c - b y}{a} = \frac{c - b (\frac{c p - a r}{b p - a q})}{a}$
$x = \frac{c b p - c a q - c b p + a b r}{a (b p - a q)}$
$x = \frac{a b r - c b p}{a (b p - a q)} = \frac{b}{a} [\frac{a r - c p}{b p - a q}]$ .

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