x-2y=6 and 3x-6y=18
no solutions
one solution
infinite solutions
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.