Question

determine a and b for which the following system of linear equations has infinite number of solutions.2x-(a-4)y=2b+1;4x-(a-1)y=5b-1.

Answer 1

aloha user!!
----------------
we are given the equations:

2x-(a-4)y=2b+1
4x-(a-1)y=5b-1

here, 
a1= 2
a2= 4
b1= -(a-4)
b2= -(a-1)
c1= 2b+1
c2= 5b - 1

----------------------------

now we know that for coincident lines:

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

-----------------------------------------------------------------------

$\frac{2}{4} = \frac{-(a-4)}{-(a-1)} = \frac{2b +1 }{5b -1}$


-----------------------------------------------------------------------

2(a- 1) = 4(a - 4)         { 2/4 = (a-4)/ a-1) }
2a - 2 = 4a - 16
2a - 4a = -16 + 2
-2a = -14
a = 7

----------------------------------------------------------------------

2( 5b - 1) = 4 ( 2b + 1 )     { 2/4 = (2b + 1)/ (5b - 1) }
10b - 2 = 8b + 4
10b - 8b = 4 + 2
2b = 6
b = 3.

---------------------------------------------------------------------
hope it helps :^)

Answer 2

Answer:

here is your answer buddy

hope it helps............