Question

what are the differences between no solution, infinitely many solutions, and one solution

Answer 1

the difference between no solution, one solution, and infinitely many solutions in the solving the system of equations

is telling what the two line are doing in relation to each other

1) if the is no solution, than the two line are Parallel to one other which is simple to show by graphing them the two line below together

graph those two line and you will see why. Okay

2x + 3 = y
2x+ 10 = y

Now if the have a solution it means the two lines cross at a point on the graph there is a solution to them that will make it true or they have a common point with each other

to see why, graph the two line equation below and you will see both lines cross at a common point on the graph which they have a one point in common to each other which will make them true to each other .Okay

2x + 3y = 10
4x + 5y = 15

The Solution is ( -2 1/2, 5)

now if they are infinite solution to them, than they are the same eact line expect one of them is written differently than the other

graph this to see why

2x + 5y = 10
10x + 25y = 50

you will find there are many answer for this

the system of equations are solve by one of the following methods

1) graphing them
2) substitution
3) elimination ( which you will learn about soon)

Solving the system of equation as many applications in the real world like navigation , map making, find relationships of things, computer graphics, design things, engineering, and other important things and that is why it important that you learn it

Answer 2

thank you this was very helpful