SOLUTION: x - y = -5 x + 2y = -4

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Question 144053: x - y = -5
x + 2y = -4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want to use substitution to solve this system.


Start with the given system of equations:

system%28x-y=-5%2Cx%2B2y=-4%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

x-y=-5 Start with the first equation


-y=-5-x Subtract x from both sides


-y=-x-5 Rearrange the equation


y=%28-x-5%29%2F%28-1%29 Divide both sides by -1


y=%28%28-1%29%2F%28-1%29%29x%2B%28-5%29%2F%28-1%29 Break up the fraction


y=x%2B5 Reduce



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

Since y=x%2B5, we can now replace each y in the second equation with x%2B5 to solve for x



x%2B2highlight%28%28x%2B5%29%29=-4 Plug in y=x%2B5 into the first equation. In other words, replace each y with x%2B5. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x%2B%282%29%281%29x%2B%282%29%285%29=-4 Distribute 2 to x%2B5


x%2B2x%2B10=-4 Multiply


3x%2B10=-4 Combine like terms on the left side


3x=-4-10Subtract 10 from both sides


3x=-14 Combine like terms on the right side


x=%28-14%29%2F%283%29 Divide both sides by 3 to isolate x



x=-14%2F3 Reduce





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


So the first part of our answer is: x=-14%2F3









Since we know that x=-14%2F3 we can plug it into the equation y=x%2B5 (remember we previously solved for y in the first equation).



y=x%2B5 Start with the equation where y was previously isolated.


y=%28-14%2F3%29%2B5 Plug in x=-14%2F3


y=-14%2F3%2B5 Multiply


y=1%2F3 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=1%2F3









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

So our answers are:

x=-14%2F3 and y=1%2F3