Question

For which values of k does the system of linear equations have zero, one, or an infinite number of solutions? [Note: Not all three possibilities need occur.] 2x1- x2= 3 , 4x1 - 2x2= k

Answer 1

• for k=6, the system has infinitely many solutions

• for k≠6, the system has no (zero) solution

Explanation:

We have the equations:

1. 
   `2x_(1) -x_(2) =3`
2. 
   `4x_(1)-2x_(2) =k`

If we multiply both sides of (1) by 2, we get
`4x_(1)-2x_(2) =6`

We also have from (2)
`4x_(1)-2x_(2) =k`

Thus if k=6, every pair (
`x_(1),x_(2)`) satisfy the equation

if k≠6, the system does not have solution.