Question

Find the value of k for which the following system of equations has infinite solutions: 4x + 2y - (k + 2) = 0 and 2x + y - 3 = 0

• A. 3
• B. 2
• C. 1
• D. 4

Answer 1

The correct option is D 4

Given two equations $a_{1}x+b_{1}y=c_{1}and{a}_{2}x+b_{2}y=c_2,$ the pair of equations will have infinite solutions if $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2},$

Thus, for the given pair of equations to have infinte solutions,
$\frac{4}{2}=\frac{2}{1}=\frac{-(k+2)}{-3}$
$\Rightarrow \frac{(k+2)}{3}=2$
$\Rightarrow k=4$