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

@e.mccormick

Answer 2

Well, there are a few ways you can get the answer. Depends on what you have been taught. Do you know what the consistent-independen etc stuff means?

Answer 3

Yes... This is in my notesConsistent system- A system of equations that has at least once solution. A pair of intersecting lines or same lines are consistent systems. Inconsistent system- A system of equations that has no solution is called an inconsistent system. Parallel lines are an inconsistent system. Dependent system- When all of the solutions on one line are the same as the other line in a system. This would create the same line. Independent system-When two lines do not share all of the same points, such as parallel lines or intersecting lines.

Answer 4

Looks good. My way of saying the same thing:

Consistent means there is one or \(\infty\) solutions.
Inconsistent means there are no solutions.
Independent means they are two lines.
Dependent means they are the same line.

consistent-independent = 2 lines that cross, one solution
consistent-dependent = the same line, \(\infty\) solutions
inconsistent-independent = 2 lines that never cross (parallel) so no solution

Now, depending on what you know how to do, you can graph the lines to see this OR you can do a little math with the equations.

Answer 5

Know why your slope-intercept form might help a lot?

Answer 6

No... Sorry I had a appointment for my teacher.

Answer 7

@e.mccormick

Answer 8

Kk.

The slope intercept form is y=mx+b where m is the slope and b is the intercept. Lets say you have two equations in this form:

\(y_1=m_1x_1+b_1\) and \(y_2=m_2x_2+b_2\) where all parts are members of the real numbers.

If \(m_1\ne m_2\) then they don't have the same slope and they are consistent-independent. That is that.

If \(m_1=m_2\) then they have the same slope and are either consistent-dependent OR inconsistent-independent.

In this second case, you look at the b part. If it also has \(b_1=b_2\) then they are the same line and consistent-dependent. If it is not equal, then you have that last choice: inconsistent-independent.