SOLUTION: Hello i would like to know how to find the answer to a problem to find if it has one solution many solutions or no solutions. The problem is 3x-6y=12 then 2x-4y=8 I know i have

Question 812249: Hello i would like to know how to find the answer to a problem to find if it has one solution many solutions or no solutions. The problem is 3x-6y=12 then 2x-4y=8 I know i have to find a b and m for these two problems. I just dont know how to do it. another problem is 2x+y=0 y=2x-4 thankyou
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
3x - 6y = 12
2x - 4y = 8
You don't have to find b or m here, just solve for x and y
Rearrange the first equation so we can use it for substitution in the 2nd equation
3x - 6y = 12
3x = 6y + 12
divide eq by 3
x = 2y + 4
:
substitute (2y+4) for x in the 2nd equation
2(2y+4) - 4y = 8
4y + 8 - 4y = 8
8 = 8, this means there is no unique solution for this system
Many values for x and y will satisfy this system of equations
:
:
2x + y = 0
y = 2x - 4
:
Substitute (2x-4) for y in the first equation
2x + (2x-4) = 0
4x = 4
x = 4/4
x = 1
find y
y = 2(1) - 4
y = 2 - 4
y = -2
:
Solution to this one: x=1, y=-2
:
Check solution in the 1st equation
2x + y = 0
2(1) + (-2) =
2 - 2 = 0; confirms our solution here

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