. Find the values of a and b for which the following system of the linear equation has infinitely many solutions (a +b)x -2by = 5a + 2b + I and 3x – y = 14
Answers
Answered by
2
ANSWER
he given system of equations is
2x+3y−7=0
2αx+(α+β)y−28=0
This system of equation is of the form
a
1
x+b
1
y+c
1
=0
a
2
x+b
2
y+c
2
=0
where a
1
=2,b
1
=3,c
1
=−7
and a
2
=2α,b
2
=(α+β) and c
2
=−28
For infinitely many solutions, we must have
a
2
a
1
=
b
2
b
1
=
c
2
c
1
The given system of equations will have infinite number of solutions, if
2α
2
=
α+β
3
=
−28
−7
⇒
α
1
=
α+β
3
=
4
1
⇒
α
1
=
4
1
and
α+β
3
=
4
1
⇒α=4 and α+β=12
⇒α=4 and β=8
Hence, the given system of equations will have infinitely many solutions, if α=4 and β=8.
Similar questions