Question

Identify whether the pair of linear equations have infinite solutions

$2x+y=1;2y=2-4x$

Answer 1

Condition for infinite solution:

For the equations: $ax+by+c=0$ and $px+qy+r=0$

$\frac{a}{p}=\frac{b}{q}=\frac{c}{r}$

Given equations:

$2x+y=1and2y=2-4x$

$\Rightarrow 2x+y-1=0and4x+2y-2=0$

Here, $a=2,b=1,c=-1$ and $p=4,q=2,r=-2$

$\frac{2}{4}=\frac{1}{2}=\frac{-1}{-2}$

Yes, the condition is satisfied,

So, the given pair of linear equation have infinite solution