Question

If the system of equations $2x+3y-5=0$, $4x+ky-10=0$ has an infinite number of solutions, then

• A. $k=\frac{3}{2}$
• B. $k\ne \frac{3}{2}$
• C. $k\ne 6$
• D. $k=6$

Answer 1

The correct option is D $k=6$

Given equations are $2x+3y-5=0$ and $4x+ky-10=0$

Then $2x+3y-5=0\Rightarrow 2x+3y=5$

$4x+ky-10\Rightarrow 4x+ky=10$

$\therefore \frac{2}{4}=\frac{3}{k}=\frac{5}{10}$ .... [Since, they have an infinite number of solutions]

$\Rightarrow \frac{1}{2}=\frac{3}{k}=\frac{1}{2}$

$\Rightarrow \frac{1}{2}=\frac{3}{k}$

$\Rightarrow k=6$