Question

Find the values of a and b respectively for which the following system of lines equations has infinite number of solutions.
$2x-3y=7$ and $(a+b)x-(a+b-3)y=4a+b$.

• A. $-1,-5$
• B. $-1,5$
• C. $1,5$
• D. $-5,-1$

Answer 1

Answer: (D)

$-5,-1$

For infinite number of solutions, the condition is:

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

$\frac{2}{a+b}$ $=\frac{3}{a+b-3}$ $=\frac{7}{4a+b}$

Solving equations simultaneously, we get two equations:

$\frac{2}{a+b}$ $=\frac{3}{a+b-3}$

$2(a+b-3)=3(a+b)$

$-a-b=6$ ........... $\left(1\right)$

$\frac{2}{a+b}$ $=\frac{7}{4a+b}$

$2(4a+b)=7(a+b)$

$a-5b=0$ ........... $\left(2\right)$

On adding these two equations, we get

$b=-1$ and $a=-5$

Hence, the answer is $-5,-1$.