Question

If $2a=b$, the pair of equations $x+2y=2a-6b,ax+by=2a^2-3b^2$ possess _____ solution(s)

• A. No
• B. Only one
• C. Only two
• D. An infinite number of slutions

Answer 1

The correct option is D An infinite number of slutions

Given $2a=b\Rightarrow a=\frac{b}{2}$

$x+2y=2a-6b$ [first given equation]

$\Rightarrow x+2y=b-6b=-5b$ ........eq(i)

$ax+by=2a^2-3b^2$ [second given equation]

$\Rightarrow \frac{b}{2}x+by=\frac{2b^2}{4}-3b^2$

$\Rightarrow \frac{bx}{2}+by=\frac{-5b^2}{2}$

$\Rightarrow bx+2by=-5b^2$ ..........eq(ii)

From (i) and (ii), Both represents same equations.

So there exits infinite number of solutions.