Question

Find the value of a and b for which the pair of linear equations xtay=b-4 and 2x+ (a+3) y=b
has infinitely many solutions​

Answer 1

Answer:

a=3

b=8

Step-by-step explanation:

for two equations to have infinite number of solutions :

a1x + b1y + c1 =0

a2x + b2y + c2 =0

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

therefore,

2x +(a+3)y-b=0

x+ay+4-b=0

on comparing with above equation :

a1=2 ,a2=1

b1=(a+3),b2=a

c1=-b,c2=4-b

hence,

$\frac{2}{1} = \frac{a + 3}{a} = \frac{ - b}{4 - b}$

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

:a=3

$2 = \frac{ - b}{4 - b}$

:b=8