Question

In each of the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:
2x+y=54x+2y=10

Answer 1

infinitely many solutions.

Step-by-step explanation:

Given:  

2x + y = 5

4x +2y = 10

So we get 2x + y - 5 = 0

 4x +2y - 10 = 0

a1 = 2, b1 = 1, c1 = -5

a2 = 4, b2 = 2, c2 = -10

a1/a2 = b1/b2 = c1/c2  = 1/2

Hence we can conclude that the given system of equation has infinitely many solutions.