Question

x-2y=6
3x-6y=18 is one solution , no solution , infinite solutions

Answer 1

This is not just one equation, but a system of two equations. We need to solve the system to determine if it has one solution, no solution, or infinite solutions.

Let's solve the system of equations:

Given the equations:
x - 2y = 6 ---(1)
3x - 6y = 18 ---(2)

We can rewrite equation (2):
3x = 6y + 18
Dividing both sides by 3, we get:
x = 2y + 6 ---(3)

Now we have two equations:
x - 2y = 6 ---(1)
x = 2y + 6 ---(3)

We can see that equation (3) is equivalent to equation (1) and thus represents the same line. This means that both equations are actually the same line and represent an infinite number of solutions.

So, the system of equations has infinite solutions.