Question

54. If the system of linear equations ax + 4y = 7 and
2x + by = 14 has infinitely many solutions, then
the value of a + b is
​

Answer 1

Solution:

Given system of equations are:-

ax + 4y = 7..................(1)

2x + by = 14.................(2)

Here,

a1=a ,a2=2 ,b1=4, b2=b ,c1=7 and c2=14

For infinitely many solutions,

a1/a2 = b1/b2 = c1/c2

Substituting the values,

=>a/2 = 4/b = 7/14

=>a/2 = 4/b = 1/2

=>a/2 =1/2 and 4/b = 1/2

=>a = 1 and b =8

This implies that for a=1 and b=8,the given system of equations have infinitely many solutions.

Now,

a + b

=1+8

=9

The answer is 9.

Answer 2

If infinite solution then,

a1/a2 =b1/b2=c1/c2

So, a/2= 4/b=7/14

a/2=4/b=1/2

4 will be simplified as 1, as b1 and c1 are equal (infinite solution)

a=1=1

2=b=2

So, a=1

But we need to multiply b with 2

b= 4×2=8

ATQ

a+b= 1+8

a+b= 9

*HOPEFULLY THIS HELP YOU*