SOLUTION: I am very confused with Algebra as a whole If someone can please help me using the substitution method with each step I would greatly appreciate it. 6x-2y=12 2x+2y=8

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: I am very confused with Algebra as a whole If someone can please help me using the substitution method with each step I would greatly appreciate it. 6x-2y=12 2x+2y=8      Log On


   

Question 481988: I am very confused with Algebra as a whole If someone can please help me using the substitution method with each step I would greatly appreciate it. 6x-2y=12 2x+2y=8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

system%286x-2y=12%2C2x%2B2y=8%29



Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the second equation

2x%2B2y=8 Start with the second equation


2y=8-2x Subtract 2x from both sides


2y=-2x%2B8 Rearrange the equation


y=%28-2x%2B8%29%2F%282%29 Divide both sides by 2


y=%28%28-2%29%2F%282%29%29x%2B%288%29%2F%282%29 Break up the fraction


y=-x%2B4 Reduce



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

Since y=-x%2B4, we can now replace each y in the first equation with -x%2B4 to solve for x



6x-2highlight%28%28-x%2B4%29%29=12 Plug in y=-x%2B4 into the first equation. In other words, replace each y with -x%2B4. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



6x%2B%28-2%29%28-1%29x%2B%28-2%29%284%29=12 Distribute -2 to -x%2B4


6x%2B2x-8=12 Multiply


8x-8=12 Combine like terms on the left side


8x=12%2B8Add 8 to both sides


8x=20 Combine like terms on the right side


x=%2820%29%2F%288%29 Divide both sides by 8 to isolate x



x=5%2F2 Reduce





-----------------First Answer------------------------------


So the first part of our answer is: x=5%2F2









Since we know that x=5%2F2 we can plug it into the equation y=-x%2B4 (remember we previously solved for y in the second equation).



y=-x%2B4 Start with the equation where y was previously isolated.


y=-5%2F2%2B4 Plug in x=5%2F2


y=3%2F2 Combine like terms (note: if you need help with fractions, check out this solver)



-----------------Second Answer------------------------------


So the second part of our answer is: y=3%2F2









-----------------Summary------------------------------

So our answers are:

x=5%2F2 and y=3%2F2

which form the point