Question

Find the value of $a$ and $b$ for which the system
$2x+3y=7$
$(a+b)x+(2a-b)y=3(a+b+1)$
will have infinite number of solutions

• A. $a=5,b=2$
• B. $a=3,b=1$
• C. $a=5,b=1$
• D. None

Answer 1

The correct option is C $a=5,b=1$

Equations have infinite number of solutions, when both the equations are same.
$\frac{a+b}{2}=\frac{2a-b}{3}=\frac{3(a+b+1)}{7}$
Now,
$\frac{a+b}{2}=\frac{2a-b}{3}$
$=>3a+3b=4a-2b$
$a=5b$
Also, $\frac{a+b}{2}=\frac{3(a+b+1)}{7}$
$7a+7b=6a+6b+6$
$a+b=6$
$=>5b+b=6$
$=>6b=6$
$=>b=1$
And $a=5b=5$