If 29x + 37y = 103 and 37x + 29y = 95 then : - Vidyadip

MCQ

If $29x + 37y = 103$ and $37x + 29y = 95$ then :

A
$x = 1, y = 2$
✓
$x = 2, y = 1$
C
$x = 3, y = 2$
D
$x = 2, y = 3$

✓

Answer

Correct option: B.

$x = 2, y = 1$

$29x + 37y = 103 ...(i)$
$37x + 29y = 95 ...(ii)$
Adding $(i)$ and $(ii),$ we get
$66x + 66y = 198$
$\Rightarrow x + y = 3 ...(iii)$
Subtract $(i)$ from $(ii),$ we get
$8x - 8y = 8$
$\Rightarrow x - y = 1 ....(iv)$
Adding $(iii)$ and $(iv),$
we get $2x = 4$
$\Rightarrow x = 2$
Substituting $x = 2$ in $(iii),$
we get $y = 1$.

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