We are given the system of equations:
y = 3x
y = 6x + 3
We can use substitution to solve this system. Since both equations are equal to y, we can set them equal to each other:
3x = 6x + 3
Subtracting 3x from both sides, we get:
0 = 3x + 3
Subtracting 3 from both sides, we get:
-3 = 3x
Dividing both sides by 3, we get:
x = -1
Now that we know x, we can use either equation to find y. Let's use the first equation:
y = 3x = 3(-1) = -3
Therefore, the solution to the system of equations is (-1, -3).
To check our solution, we can substitute these values back into both equations:
y = 3x gives us -3 = 3(-1), which is true
y = 6x + 3 gives us -3 = 6(-1) + 3, which is also true
Therefore, our solution is correct.
We can also plug in the other given points to check that they do not satisfy both equations, which means they are not solutions to the system.