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?​

Answer 1

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Answer 2

Concept introduction:

If the two lines that are represented by the equations $ax + by + c = 0$ and $dx + ey + g = 0$ cross at a point, then the system of linear equations $ax + by + c = 0$ and $dx + ey + g = 0$ will have a unique solution. if neither of the two lines is parallel nor coinciding.

Explanation:

Given that, two equations $ax + by - (a - b) = 0$ and $bx + ay - (a + b) = 0$

We have to find, possible values of a and b so that they have unique solution.

According to the question,

The two lines have unique solution if, $\frac{a}{b} =\frac{b}{a}$

⇒$a^{2} =b^{2}$

Final Answer:

If $a^{2} =b^{2}$ then the two given lines have unique solution.

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