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

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)   (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
---------
Then 4x = 2x+6 (they both = y)
2x = 6
x = 3
y = 12

Answer by gonzo(654)   (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)   (Show Source): You can put this solution on YOUR website!
This is a "systems of linear equations" problem, but that's ok.

Start with the second equation

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

Subtract from both sides.

Combine like terms on the left side.

Divide both sides by to isolate .

Reduce.

So the first part of the answer is

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

Go back to the first equation.

Plug in (the previous solution)

Multiply

So the second part of the answer is

=============================================================

Answer:

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