Question

Consider the following statements:

Statements I: When two simultaneous equations are added or subtracted, the resulting solution does not change.

Statements II: When one of the two simultaneous equations is multiplied with a constant and added with the other equation, the resulting solution does not remain same.

Choose the correct option based on the statements.

• A. Both the statements are correct.
• B. Only statement I is correct.

Answer 1

The correct option is B Only statement I is correct.

When two simultaneous equations are added or subtracted, or multiplied with a constant and added or subtracted, the resulting solution does not change.

Let's take an example.
$2x+y=4...\left(a\right)$
$x-y=5...\left(b\right)$
The solution of these equations is obtained by substitution method as follows:
$2(5+y)+y=4$
$\Rightarrow 10+2y+y=4$
$\Rightarrow 3y=4-10$
$\Rightarrow y=-\frac{6}{3}$
$\Rightarrow y=-2$
$\Rightarrow x=5+y=5-2=3$
$(3,-2)$ is the solution.

Let's multiply a constant, $2$ with $\left(b\right)$ and subtract it from $\left(a\right).$

$\Rightarrow 2x+y-2(x-y)=4-2\left(5\right)$
$\Rightarrow 2x+y-2x+2y=4-10$
$\Rightarrow 3y=-6$
$\Rightarrow y=-2$
$\Rightarrow x=3$

Again we obtain the same solution.
$\therefore$ Statements I is correct, and Statements II is wrong.