Solve for $x, y :$
$(a + 2 b) x + (2 a - b) y = 2, (a - 2 b) x + (2 a + b) y = 3$ .

x = (5 b - 2 a), y = 10 a b

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = \frac{5 b - 2 a}{10 a b}, y = \frac{a + 10 b}{10 a b}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

x = \frac{5 b - 2 a}{10 a b}, y = \frac{5 a + 10 b}{10 a b}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = \frac{5 b + 2 a}{10 a b}, y = \frac{a + 10 b}{10 a b}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $x = \frac{5 b - 2 a}{10 a b}, y = \frac{a + 10 b}{10 a b}$
$(a + 2 b) x + (2 a - b) y = 2$
$\Rightarrow y = \frac{2 - a x - 2 b x}{2 a - b} (a - 2 b) x + (2 a + b) y = 3$
$\Rightarrow (a - 2 b) x + (2 a + b) \times \frac{2 - a x - 2 b x}{2 a - b} = 3$
$\Rightarrow \frac{(a x - 2 b x) (2 a - b) + (2 a + b) (2 - a x - 2 b x)}{2 a - b} = 3$
$\Rightarrow 2 a^{2} x - 4 a b x - a b x + 2 b^{2} x + 4 a + 2 b - 2 a^{2} x - a b x - 4 a b x - 2 b^{2} x = 3 (2 a - b)$
$\Rightarrow 4 a + 2 b - 10 a b x = 6 a - 3 b$
$\Rightarrow 2 a - 5 b + 10 a b x = 0$
$\Rightarrow x = \frac{5 b - 2 a}{10 a b} y = \frac{2 - a (\frac{5 b - 2 a}{10 a b}) - 2 b (\frac{5 b - 2 a}{10 a b})}{2 a - b}$
$\Rightarrow y = \frac{2 (10 a b) - a (5 b - 2 a) - 2 b (5 b - 2 a)}{10 a b} \times \frac{1}{2 a - b}$
$\Rightarrow y = \frac{20 a b - 5 a b + 2 a^{2} - 10 b^{2} + 4 a b}{10 a b \times (2 a - b)}$
$\Rightarrow y = \frac{19 a b + 2 a^{2} - 10 b^{2}}{10 a b \times (2 a - b)}$
$\Rightarrow y = \frac{a + 10 b}{10 a b}$

Suggest Corrections