SOLUTION: 1.Without graphing, determine whether each system has one solution, no solutions, or an infinite number of solutions. Show your work. (2 marks each) ( a ) 4 x – y = 5

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 1.Without graphing, determine whether each system has one solution, no solutions, or an infinite number of solutions. Show your work. (2 marks each) ( a ) 4 x – y = 5       Log On


   

Question 320609: 1.Without graphing, determine whether each system has one solution, no solutions, or an infinite number of solutions. Show your work. (2 marks each)
( a ) 4 x – y = 5
y = 4 x + 6



( b )3x + 2y = 5
15x + 10y = 25












2. How can you tell by looking at an equation whether it has one, none or infinite solutions?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


One question per post, please.

If you have a system:





and the coefficients are such that:

and

but

then you have a system that is inconsistent, i.e., has no solutions. (parallel lines)

If the coefficients are such that:

and

and

then you have a system that is consistent and dependent, i.e. there are infinite solutions (the same line)


If the coefficients are such that:

but ,

then you have a consistent and independent system, i.e. exactly one solution (intersecting lines)



John