Question

Solve for x and y:
$\frac{2x}{a}+\frac{y}{b}=2$
$\frac{x}{a}-\frac{y}{b}=4$

• A. x = 2a, y = -2b
• B. x = 3a, y = -3b
• C. x = 3a, y = -2b
• D. Insufficient data
• E. None of the above

Answer 1

The correct option is A x = 2a, y = -2b

The given equations are

$2\frac{x}{a}+\frac{y}{b}=2\dots \dots \left(1\right)$

$\frac{x}{a}-\frac{y}{b}=6\dots \dots \left(2\right)$

Adding (1) and (2), we get

$3\frac{x}{a}=6\Rightarrow 3x=6a\Rightarrow x=\frac{6a}{3}=2a$

Putting x = 2a in (1), we get

$2\frac{2a}{a}+\frac{y}{b}=2\Rightarrow 4+\frac{y}{b}=2$

$\Rightarrow \frac{y}{b}=2-4=-2$

$\Rightarrow y=-2b$

Hence, the required solution is x = 2a, y = -2b