Question

Find the value of a and b for which the following system of linear equations has infinitely many solutions.

$(a-1)x+3y=26x+(1-2b)y=6$

• A.
  3 and -4
• B.
  4 and -3
• C.
  2 and 1
• D.
  7 and 4

Answer 1

The correct option is A

3 and -4
$(a-1)x+3y=\mathrm{2...}\left(1\right)6x+(1-2b)y=\mathrm{6.....}\left(2\right)$

For infinitely many solutions, we must have

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\Rightarrow \frac{a-1}{6}=\frac{3}{1-2b}=\frac{-2}{-6}\frac{a-1}{6}=\frac{-2}{-6}\Rightarrow a-1=2\Rightarrow a=2+1\Rightarrow a=3And,\frac{3}{1-2b}=\frac{-2}{-6}\Rightarrow 9=1-2b2b=1-9\Rightarrow 2b=-8\Rightarrow b=\frac{-8}{2}\therefore b=-4$