Question

What are the value of a and b for which the following system of linear equation has consistent & dependent solutions
2x - 3y = 7 ; (a + b) x - (a + b - 3) y = 4a + b

• A. $a=-3,b=-1$
• B. $a=-1,b=-3$
• C. $a=-5,b=-1$
• D. $a=-1,b=-5$

Answer 1

Answer: (C)

$a=-5,b=-1$

Equations have consistent & dependent solutions, when both the equations are same or a multiple of the other.
$\frac{a+b}{2}=\frac{a+b-3}{3}=\frac{4a+b}{7}$
Now,
$\frac{a+b}{2}=\frac{a+b-3}{3}$


$=>3a+3b=2a+2b-6$


$a+b=-6$ -- (1)
Also, $\frac{a+b}{2}=\frac{4a+b}{7}$


$7a+7b=8a+2b$


$a=5b$ --- (2)

From equations $1$ and $2$, we get


$=>5b+b=-6$


$=>6b=-6$


$=>b=-1$

And $a=5b=-5$