SOLUTION: Solve the system by the substitution method. -2x + y = -2 x - 4y = 9

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Question 398681: Solve the system by the substitution method.
-2x + y = -2
x - 4y = 9
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%28-2x%2By=-2%2Cx-4y=9%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 first equation

-2x%2By=-2 Start with the first equation


y=-2%2B2x Add 2x to both sides


y=2x-2 Rearrange the equation

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

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



x-4highlight%28%282x-2%29%29=9 Plug in y=2x-2 into the second equation. In other words, replace each y with 2x-2. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x%2B%28-4%29%282%29x%2B%28-4%29%28-2%29=9 Distribute -4 to 2x-2


x-8x%2B8=9 Multiply


-7x%2B8=9 Combine like terms on the left side


-7x=9-8Subtract 8 from both sides


-7x=1 Combine like terms on the right side


x=%281%29%2F%28-7%29 Divide both sides by -7 to isolate x



x=-1%2F7 Reduce





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


So the first part of our answer is: x=-1%2F7









Since we know that x=-1%2F7 we can plug it into the equation y=2x-2 (remember we previously solved for y in the first equation).



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


y=2%28-1%2F7%29-2 Plug in x=-1%2F7


y=-2%2F7-2 Multiply


y=-16%2F7 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=-16%2F7









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

So our answers are:

x=-1%2F7 and y=-16%2F7

which form the point



If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim