Question

Two different equations can never have the same answer. State whether the statement is true (T) or false (F).

• A. True
• B. False

Answer 1

The correct option is B False

Verify the given statement:

Given statement is two different equations can never have the same answer.

Case 1: Consider the equations $5x-6=0$ and $8x-9=0$

$\begin{array}{crcccrcc}& 5x-6& =& 0& & 8x-9& =& 0\\ \Rightarrow & 5x& =& 6& \Rightarrow & 8x& =& 9\\ \Rightarrow & x& =& \frac{6}{5}& \Rightarrow & x& =& \frac{9}{8}\end{array}$

Here we can observe that two different equations $5x-6=0$ and $8x-9=0$ have different answers i.e. $\frac{6}{5}$ and $\frac{9}{8}$ respectively.

Case 2: Consider the equations $6x-18=0$ and $8x-24=0$

$\begin{array}{crcccrcc}& 6x-18& =& 0& & 8x-24& =& 0\\ \Rightarrow & 6x& =& 18& \Rightarrow & 8x& =& 24\\ \Rightarrow & x& =& \frac{18}{6}& \Rightarrow & x& =& \frac{24}{8}\\ \Rightarrow & x& =& 3& \Rightarrow & x& =& 3\end{array}$

Here we can observe that two different equations $6x-18=0$ and $8x-24=0$ have same answer i.e. $3$.

Considering case 1 and case 2, we can say that two different equations can have the same answer.

Hence the given statement is false.