Question

$I.$ If $3x-5y=-1$ and $x-y=-1$, then $x=-2,y=-1$
$II.$ $2x+3y=9,3x+4y=5\Rightarrow x=-21,y=17$
$III.$ $\frac{2x}{a}+\frac{y}{b}=2,\frac{x}{a}-\frac{y}{b}=4\Rightarrow x=2a,y=2b$
What is true ?

• A. $I$
• B. $II$
• C. $III$
• D. None of these

Answer 1

Answer: (A), (B)

The correct options are
A $I$
B $II$

Let $3x-5y=-1$ ......(1)
$x-y=-1$ ......(2)
(1) $-$ (2) $\times 3$

$\Rightarrow -2y=2$
$\Rightarrow y=-1$
Substituting the value of $y$ in (2)

$\Rightarrow x+1=-1$

$\Rightarrow x=-2$
$\therefore I$ is true.
Let $2x+3y=9$ ......(1)
$3x+4y=5$ ......(2)
(1) $\times 3-$ (2) $\times 2$

$\Rightarrow y=17$
Substituting the value of $y$ in (1)
$\Rightarrow 2x+3\left(17\right)=9$
$\Rightarrow 2x=-42$
$\Rightarrow x=-21$
$\therefore II$ is true.
Let $\frac{2x}{a}+\frac{y}{b}=2$ ......(1)
$\frac{x}{a}-\frac{y}{b}=4$ ......(2)
(1) $-$ (2) $\times 2$

$\Rightarrow \frac{3y}{b}=-6$

$\Rightarrow y=-2b$
Substituting the value of $y$ in (2)
$\Rightarrow \frac{x}{a}+\frac{2b}{b}=4$
$\Rightarrow x=2a$
$\therefore III$ is false.