Question

Which of the following are possible values of a and b if equations ax + by - (a - b) = 0 and bx + ay - (a + b) = 0 have a unique solution?

• A. a = 0, b = 0
• B. a = 2, b = - 2
• C. a = 1, b = 2
• D. a = 1, b = 1

Answer 1

The correct option is C a = 1, b = 2

Given two equation $a_{1}x+b_{1}y+c_1=0and{a}_{2}x+b_{2}y+c_2=0$
the pair of equations will have a unique solution if $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$.

Thus, for the given pair of equations to have a unique solution.
$\frac{a}{b}\ne \frac{b}{a}$
$\Rightarrow a^2\ne b^2$
Among the given options, only a = 1, b = 2 satisfies this condition.