SOLUTION: solve the systems of equations using addition to elimiate one variable. if the system has no solution,indicate that it is inconsistent;if it has infinate solutions,indicate that it

Question 773076: solve the systems of equations using addition to elimiate one variable. if the system has no solution,indicate that it is inconsistent;if it has infinate solutions,indicate that it is dependent;if the system has one soulution,check your answer.
5. -y=2x 3x+y=20

6. 4x+2y=6 2x+y=3

please i really need help, if i can get this to problems done i can graduate. im not sure how do do theses problems please and thank you for your help.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
5.
-y = 2x
3x + y = 20
rearrange the 1st equation so we have:
2x + y = 0
Subtract this from the 2nd equation
3x + y = 20
2x + y = 0
--------------Subtracting eliminates y find x
x = 20
find y using the 1st equation (rearranged)
2x + y = 0
Replace x with 20
2(20) + y = 0
40 + y = 0
Subtract 40 from both sides
y = -40
It has one solution
:
Check this in the 2nd equation
3x + y = 20
Replace x and y
3(20) - 40 = 20; confirms our solutions of x=20; y=-40
:
:
6.
4x + 2y = 6
2x + y = 3
these are the same equation, if you mult the 2nd eq by 2 you get the 1st eq
therefore it has infinite solutions
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