Final answer:
The lines y = 3x + 1 and -3x - 6y = -27 intersect at the point (-7/114, -2/19).
Step-by-step explanation:
To find the point of intersection between the lines y = 3x + 1 and -3x - 6y = -27, we can set the two equations equal to each other:
3x + 1 = -3x - 6y
Now, we can solve for x:
3x + 3x = -1 - 6y
6x = -1 - 6y
6x + 6y = -1
Next, we can substitute the value of x into one of the original equations to solve for y:
y = 3x + 1
y = 3(-1 - 6y) + 1
y = -3 - 18y + 1
19y = -2
y = -2/19
Now, we can substitute the value of y back into the equation 3x + 1 = -3x - 6y to solve for x:
3x + 1 = -3x - 6(-2/19)
3x + 1 = -3x + 12/19
6x = 12/19 - 1
6x = -7/19
x = -7/114
Therefore, the lines y = 3x + 1 and -3x - 6y = -27 intersect at the point (-7/114, -2/19).