Question

How many solutions does the system of equations have ? Y= 6x +2 and 3y-18x=12

Answer 1

Answer:

0 solutions

Step-by-step explanation:

same slope, different y intercepts so they never intersect

Answer 2

Answer:

As both slopes are equal, and the values of b are different it means that the two lines are parallel and the system of equations does not have any solution. (Please see the picture below)

Step-by-step explanation:

1. First write the system of equations:

$y=6x+2$

$3y-18x=12$

2. Solve y for the second equation:

$3y-18x=12$

$3y=18x+12$

$y=\frac{18x+12}{3}$

$y=6x+4$

3. Re write both equations in the form y=mx+b, where m is the slope and b is the value of y when x=0 :

$y=6x+2$

$y=6x+4$

As both slopes are equal, and the values of b are different it means that the two lines are parallel and the system of equations does not have any solution.