Question

MEDALS ARE GIVEN! PLEASE HELP!
Several systems of equations are given below.
System A
y = 6x – 1.5
y = –6x + 1.5
System B
x + 3y = –6
2x + 6y = 3
System C
2x –y = 5
6x – 3y = 15
Which system of equations is consistent-independent? How many solutions will the system of equations have? Expain your answers.
Which system of equations is consistent-dependent? How many solutions will the system of equations have? Expain your answers.
Which system of equations is inconsistent-independent? How many solutions will the system of equations have? Expain your answers.

Answer 1

An independent system will have different slopes and one solution.
A dependent system will have same slope and same y intercept because they are the same line and will have infinitely many solutions.
An inconsistent system will have same slope but different y intercepts because the lines will be parallel and will have no solutions.

Answer 2

So, basically you need to find the slopes and the y intercepts of all these equations to be able to find your answers. By putting the equations in y = mx + b form, where m is your slope and b is your y intercept, you can find the answers you are looking for.

Answer 3

thank you!