SOLUTION: Question: Create systems of linear equations with each possible number of solutions. 1. Consistent System (or one solution): 2. Inconsistent Graph (or no solutions): 3. D

Question 57068: Question:
Create systems of linear equations with each possible number of solutions.
1. Consistent System (or one solution):
2. Inconsistent Graph (or no solutions):
3. Dependent Equation (or infinitely many solutions):
I know an example is required here, but how do you figure it out? I'm not used to making my own problems up, any help would be appreciated.

Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
Question:
Create systems of linear equations with each possible number of solutions.
1. Consistent System (or one solution):
These two lines intersect at exactly one point.
A consistent system would include two lines with different slopes.
The slope intercept form of a line is: , where m=slope and (0,b)=y-intercept.
In a consistent system, the slope of L1) would not equal the slope of L2). (m1 not=m2)
Ex.
L1)
L2)
m1=2 and m2=3
2 does not = 3
2. Inconsistent Graph (or no solutions):
These two lines are parallel and never intersect.
m1=m2, but (0,b1) does not = (0,b2)
Ex.
L1)
L2)
m1=2 and m2=2, 2=2.
but b1=4 and b2=5, 4 not=5
Notice that you'd have to either have these lines in slope intercept form to recognize this, or if you tried to solve it, your variables would be eliminated and you'd be left with two numbers that are not equal equal to each other. In this case (4=5) or (0=1), depending on the method you use.
3. Dependent Equation (or infinitely many solutions):
These two lines are lying right on top of each other and have all points in common.
m1=m2 and b1=b2
L1)y=2x+4
L2)y=2x+4
m1=2 and m2=2, 2=2
b1=4 and b2=4, 4=4
This is obvious when the lines are in slope intercept form and simplified, but:
These same lines can be written as:
L1) -2x+y=4
L2) -4x+2y=8
If you tried to solve it, your variables would be eliminated and you'd get 0=0, or 4=4, something that ='s itself.
I hope that helps you to pick your own lines.
Happy Calculating!!!

RELATED QUESTIONS
3. this one I just don't understand. Please help if you can. 1. How many... (answered by eperette)

create systems of linear equations with each possible number of solutions (answered by Alan3354)

How would each possible number of solutions appear graphically? Create systems of linear (answered by jim_thompson5910)

For each system of linear equations shown below, classify the system as "consistent... (answered by stanbon)

Hello out there,I really need some help with some tough problems,the first one is Solve... (answered by cheesey)

Consider the equation 3x+2y=6. If possible, find a second linear equation to create a... (answered by Fombitz)

4x-4/3y=-2 -16+16/3y=8 the given system of linear equations has one solution, no... (answered by lwsshak3)

This is from a mom trying to help child with algebra - the question: Solve the system... (answered by stanbon)