Question

For the pair of equations
$x+3y=7;2x+6y=m$
to have infinitely many solutions, the value of $m$ should be $5$. Is the statement true?

Answer 1

Given equations

$x+3y=7⟶\left(1\right),2x+6y=m⟶\left(2\right)$

Equation $\left(2\right)$ can be written as $x+3y=\frac{m}{2}$

The two equations $a_{1}x+b_{1}y=c_1$ and $a_{2}x+b_{2}y=c_2$

will have infinitely no of solutions if

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

So, from given equations,

$\frac{1}{1}=\frac{3}{3}=\frac{7\left(2\right)}{m}$

$⟹14=m$

The value of $m$ is $14$. So, the given statement is false.