SOLUTION: I apologize if this is in the wrong heading. My problem is systems of linear equation by substitution. { y=4x { y=2x+6 I am not sure how to do this problem. I tried getting the

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: I apologize if this is in the wrong heading. My problem is systems of linear equation by substitution. { y=4x { y=2x+6 I am not sure how to do this problem. I tried getting the      Log On


   

Question 171363: I apologize if this is in the wrong heading. My problem is systems of linear equation by substitution. { y=4x { y=2x+6
I am not sure how to do this problem. I tried getting the numbers to match up so i could figure it out, but i cant seem to grasp it. Sorry if you cannot solve this problem and i'm sorry for wasting your time, but i am about ready to give up. This is a worksheet, and not from a book, by the way.
Found 3 solutions by Alan3354, gonzo, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
My problem is systems of linear equation by substitution. { y=4x { y=2x+6
----------------
y=4x
y=2x+6
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Then 4x = 2x+6 (they both = y)
2x = 6
x = 3
y = 12



Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
your 2 equations are:
y = 4x
y = 2x+6
since both equations equal to y, then they both must be equal to each other.
so.......
4x = 2x + 6
-----
this is the same as saying substitute 4x for y in the second equation because y = 4x from the first equation.
-----
4x = 2x + 6
simplify:
2x = 6
x = 3
-----
now you have x, you can solve for y.
in the first equation.
y = 4x
y = 4*3)
y = 12
-----
in the second equation.
y = 2x + 6
y = 2*3 + 6
y = 6 + 6
y = 12
-----
you get the same value of y and x in both equation so you have solved them simultaneously.
x = 3
y = 12
-----

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
This is a "systems of linear equations" problem, but that's ok.



y=2x%2B6 Start with the second equation


4x=2x%2B6 Plug in y=4x (the first equation). What's going on here is we're simply replacing "y" with "4x". This is where the "substitution" comes in.


4x-2x=6 Subtract 2x from both sides.


2x=6 Combine like terms on the left side.


x=%286%29%2F%282%29 Divide both sides by 2 to isolate x.


x=3 Reduce.


So the first part of the answer is x=3



--------------------------------------------



y=4x Go back to the first equation.


y=4%283%29 Plug in x=3 (the previous solution)


y=12 Multiply


So the second part of the answer is y=12


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Answer:


So the solutions are x=3 and y=12 which form the ordered pair (3,12)