Ok, I was sick for a while and I talked to the teacher about it. He explained it to me but he is a horrible explainer so I never really got what he said. So he told me to look in the text book and I still don't get it.. Do you think you can help?

graph each system of equations using the coordinate plane provided. Then determine whether the system has one solution, no solution, or infinitely man solutions. If the solution has one, name it.

x+y=3
x-y=3

2x-y=6
4x-2y=12

x+y=0
x+y=2


Do you think you could do two of those and make a graph of it on photoshop for me? You know, like make a grid and plot the lines? I just need examples so I can figure out the rest. There is a whole sheet of the things I need to do..

well i know that you need to set everything equal to y. so for the first one, you would switch it around so that it looks like this:

x+y=3 --> y=3-x [i just subtracted x from both sides]
x-y=3 --> y=x-3 [same idea]

then you graph it and see if they intersect. this one intersects once, so it has one solution. if they don't intersect, there's no solution. and i forgot what happens if there's many solutions.

x+y=3
x-y=3

2x-y=6
4x-2y=12

x+y=0
x+y=2


What you would have to do for these is use the Elimination method for solving equations. The first one is already set up to use this method. To do this you would do the following:

1) Add the variables horizonally so that one variable crosses out (y's in this case)

x+y=3
x-y=3
2x=6

2) Solve that equation.

x=3

3) Then you would put x back in one of the equations to find y. So you would end up getting 3+y=3, therefore y=0. And your point of intersection would be (3,0).

The next one is a little harder because the equations are not set up so that 1 of the variables will cancel out. So you would have to do this:

1) Multiply or Divide 1 or both equations by a certain number to get one of the variables to cross out when added. For this one I'm going to multiply the 1st fraction by -2.

2x-y=6
4x-2y=12

-becomes-

-4x+2y=-12
4x-2y=12

2) Add

-4x+2y=-12
4x-2y=12
0=0

3) Everything cancels out so therefore, there is no point that they intersect at and they are therefore parallel.

The last one is just like the second.

look here ill do an example for you

4x-2y=12
since its an equation of a line then its easy...

just findthe x and y intercepts

you find the x intercept by making y=0

thus 4x-2(0)=12 ...

thus it goes to 4x=12

then x=12/4

x=3

then find the y intercept by making x=0

hence -2y=12

then y=12/-2

y=-6

thus the intercepts are at (3,0) and (0,-6)

then sketch (see bottom of post.. but i hope you fill the grpah in better than me and do it to scale)

its dodgy but it explains a whole lot... see ive done the most difficult one and the others are soo simple


you can only have multiple answers if its a parabola of quadratic or cubic... but these are simple line graphs and are very straight forward and have only one answer... and the line will always intersect the x and y axis unless you have the equations of y=0, x=0 or x=y

Oooo i'm learning this in AlgII alsooooo. I feel so useful. Anyways.. everyone's directions here seem pretty right.. buttttt I have the ultimate secret. If you have a TI calculator (82+ or something*) you can put the equation in "Y=" form.. then "graph" press "2nd+Trace" "number 5" then press "enter" three times. or until it shows the intersection.. veryyyy useful on tests.

Parallel lines have no solution.
Coinciding lines have infinite solutions.
Intersecting lines have one solution.

Good luck