Question

The solution set of the following linear equations
$2x-5y+4=0$, $2x+y-8=0$ is

• A. $x=3,y=2$
• B. $x=3,y=4$
• C. $x=1,y=2$
• D. $x=1,y=3$

Answer 1

The correct option is A $x=3,y=2$

Given,

$2x-5y=-4$ ....(1)

$2x+y=8$ ....(2)

Subtracting equation 2 from 1, we get,

$2x+y-(2x-5y)=8-(-4)$

$\Rightarrow 2x+y-2x+5y=8+4$

$\Rightarrow 6y=12$

$\Rightarrow y=2$

Now putting value of $y$ in equation (2)
$2x=8-y$.......from(2)

$\Rightarrow x=\frac{8-y}{2}$

$\Rightarrow x=\frac{8-2}{2}=\frac{6}{2}=3$

$\therefore x=3$

So, we get that $x=3$ and $y=2$

Hence, the option is $A$