Question

Solve the equations using elimination method:
$x+y=2$ and $2x+4y=6$

• A. $(-1,-1)$
• B. $(1,1)$
• C. $(-1,1)$
• D. $(1,-1)$

Answer 1

Answer: (B)

$(1,1)$

$x+y=2$ .....(1)
$2x+4y=6$ .....(2)
Multiply equation (1) by $4$ and then subtract the equation
$4x+4y=8$ ......(3)
$2x+4y=6$ .....(4)
(-) (-) (-)
_____________
$2x=2$
$\Rightarrow x=\frac{2}{2}$
$\Rightarrow x=1$
Put the value of $x=1$ in equation (1), we get
$x+y=2$
$\Rightarrow 1+y=2$
$\Rightarrow y=2-1$
$\Rightarrow y=1$
Therefore, the solution is $(1,1)$.