Question

Find the solution for the pair of linear equations:
$2x+4y=12$
$4x+2y=18$

• A. $(1,4)$
• B. $(2,2)$
• C. $(4,1)$
• D. $(1,1)$

Answer 1

The correct option is C

$(4,1)$

Given that,
$2x+4y=12$
$\Rightarrow 2x=12-4y$
$\Rightarrow x=\frac{12-4y}{2}$
$\Rightarrow x=6-2y$ .................(i)

Now putting this value of $x$ in the second equation,
$4x+2y=18$,
we get:

$4(6-2y)+2y=18$
$\Rightarrow 24-8y+2y=18$
$\Rightarrow 6y=6$

Thus, $y=1$

Now, putting this value of $y$ in equation (i), we get,
$x=6-2\left(1\right)$
$\Rightarrow x=4$