SOLUTION: Hello out there,I really need some help with some tough problems really bad,the first one is,Determine whether the system has one solution,no solution,or infinitely many solutions:

Question 106473: Hello out there,I really need some help with some tough problems really bad,the first one is,Determine whether the system has one solution,no solution,or infinitely many solutions:y=2/3x and 2x-y=-4.The next one is,Determine whether the system has one solution,no solution,or infinitely many solutions:y=-x+2 and 3x+3y=6.The next one is,State whether the system is consistent and independent,consistent and dependent,or inconsistent:x+y=4 and 2x-y=-7.And the last one is,State whether the system is consistent and independent,consistent and dependent,or inconsistent:4x+2y=8 and 2x+y=1.Thanks to whoever can help me.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
All you have to do to answer the above questions is get both equations in the slope-intercept form: y=mx+b
m is the slope if m is different in each equation then the system is consistent and the system has an answer and the lines cross on the graph.
If m is the same number (including sign) in both equations:
I) If b is different in both equations then there is no answer and the graph shows parallel lines and the system is inconsistent.
II) if b is equal in both equations then the equations are equal and consistent and has an infinate number of answers.
.
y=2/3x
2x-y=-4...-y=-2x-4...y=2x+4
m=2/3 in the 1st equ. and 2x in the 2nd so they are consistent and there is a solution.

.
y=-x+2
3x+3y=6...3y=-3x+6...y=-x+2
These are the same equation. infinate number of answers.
.
x+y=4...y=-x+4
2x-y=-7...-y=-2x-7...y=2x+7
Has a solution
.
4x+2y=8...2y=-4x+8...y=-2x+4
2x+y=1...y=-2x+1
slopes are equal; b's are different.
inconsistent, parallel lines

.
Not hard at all, once you know how to do them, huh.
.
Ed

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