Solve for $^{'} x^{'}$ and $^{'} y^{'}$ $4 x + 7 y = 20$ , $21 x - 13 y = 21$

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Solution

$4 x + 7 y = 20 ⟶ (i) 21 x - 13 y = 21 ⟶ (i i)$
Multiplying $(i)$ by $21$ and $(i i)$ by $4.$
$84 x + 147 y = 420 ⟶ (i) 84 x - 52 y = 84 ⟶ (i i)$
On substraction : $199 y = 336 y = \frac{336}{199}$
Putting the value of $y ⟶ (i)$
$4 x + 7 \times \frac{336}{199} = 20 \Rightarrow 4 x = 20 - 7 \times \frac{336}{199} \Rightarrow 4 x = \frac{3980 - 2352}{199} ∴ x = \frac{1628}{4 \times 199} x = \frac{407}{199}$

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