Question

2a+5b=1 & 60a+40b=19, find a & b

Answer 1

Given,
2a + 5b= 1,

4a + 10b= 2...............(I)
and
60a +40b= 19

→10(6a + 4b)= 19

→6a+ 4b= 19/10

→2(3a + 2b)= 19/10

→3a +2b= 19/20

→15a +10b = 19*5/20


→15a +10b =19/4....................(ii).
Now,
Equation (ii) - (I)

→11a = 19/4 -2

→11a = 11/4

→a= 1/4

putting a= 1/4 in equation 2a+5b=1., We get,
2*1/4. +5b= 1
→1/2 +5b= 1

→5b= 1 - 1/2

→5b= 1/2

→b= 1/10.
Hence,
a=1/4
b=1/10

Answer 2

the given equations are.
2a+5b=1 ...........(i)
60a+40b=19 .........(ii)
multiplying (i) by 8 and subtract the results,we get
a=9/5
put the value of a in eqn (i)
2a+5b=1
18/5+5b=1
5b=1-18/5
5b=-13/5
so, b=-13/25