Simple Linear Equations — Statement I-II Type Questions

Statement 1: An equation remains unchanged (or unaltered), when both the sides of the equation are divided by the same non-zero number.

Statement 2: A number $n$ is a root (solution) of the equation $ax + b$ = 0, $a$ ≠ 0, $'a'$ and $'b'$ are real numbers, if and only if

$an + b = 0 ⇒ n = -\dfrac{b}{a}, a \neq 0.$

Which of the following options is correct?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Answer

Dividing both the sides of an equation by the same non-zero number does not change the equation. Hence, Statement 1 is true.

If $n$ is a root of $ax + b$ = 0, then $an + b$ = 0, which gives $n = -\dfrac{b}{a}, a \neq 0$. Hence, Statement 2 is true.

Hence, option 1 is the correct option.