x-2y=6 and 3x-6y=18

Question

no solutions

one solution

infinite solutions

Answer 1

The given system of equations is:

1) x - 2y = 6
2) 3x - 6y = 18

To determine the number of solutions, we can manipulate these equations:

For equation 1, let's solve it for x:
x = 2y + 6

Substitute this value of x into equation 2:
3(2y + 6) - 6y = 18
6y + 18 - 6y = 18
18 = 18

As a result, we see that the equations are dependent and the consistent solution set is infinite solutions.