Question:
if the system of equations 2x +3y = 7 and (a-b)x +(2a-b)y = 21 has infinitely many solutions. find the value of a and b.
Answer:
We have,
(a - b)x + (2a - b)y = 21
2x + 3y = 7
For the above equations to have infinitely many solutions,
(a - b)/2 = (2a - b)/3 = 21/7 = 3
we get:
a - b = 6 . . . . . (i)
2a - b = 9 . . . . (ii)
Now, subtracting (i) from (ii):
a = 3,
Substituting a = 3 in (i), we get
3 - b = 6
b = - 3
So, we get a = 3, and b = - 3.
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