SOLUTION: Solve each of the following systems by substitution. 5x - 2y=-5 y - 5x = 3

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Question 126352:
Solve each of the following systems by substitution.
5x - 2y=-5 y - 5x = 3
Found 2 solutions by jim_thompson5910, checkley71:
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%285x-2y=-5%2C-5x%2By=3%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

5x-2y=-5 Start with the first equation


-2y=-5-5x Subtract 5x from both sides


-2y=-5x-5 Rearrange the equation


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


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


y=%285%2F2%29x%2B5%2F2 Reduce



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

Since y=%285%2F2%29x%2B5%2F2, we can now replace each y in the second equation with %285%2F2%29x%2B5%2F2 to solve for x



-5x%2Bhighlight%28%28%285%2F2%29x%2B5%2F2%29%29=3 Plug in y=%285%2F2%29x%2B5%2F2 into the first equation. In other words, replace each y with %285%2F2%29x%2B5%2F2. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



%282%29%28-5x%2B%285%2F2%29x%2B5%2F2%29=%282%29%283%29 Multiply both sides by the LCM of 2. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



-10x%2B5x%2B5=6 Distribute and multiply the LCM to each side



-5x%2B5=6 Combine like terms on the left side


-5x=6-5Subtract 5 from both sides


-5x=1 Combine like terms on the right side


x=%281%29%2F%28-5%29 Divide both sides by -5 to isolate x



x=-1%2F5 Reduce





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


So the first part of our answer is: x=-1%2F5









Since we know that x=-1%2F5 we can plug it into the equation y=%285%2F2%29x%2B5%2F2 (remember we previously solved for y in the first equation).



y=%285%2F2%29x%2B5%2F2 Start with the equation where y was previously isolated.


y=%285%2F2%29%28-1%2F5%29%2B5%2F2 Plug in x=-1%2F5


y=-5%2F10%2B5%2F2 Multiply


y=2 Combine like terms and reduce. (note: if you need help with fractions, check out this solver)



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


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









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

So our answers are:

x=-1%2F5 and y=2

which form the point








Now let's graph the two equations (if you need help with graphing, check out this solver)


From the graph, we can see that the two equations intersect at . This visually verifies our answer.




graph of 5x-2y=-5 (red) and -5x%2By=3 (green) and the intersection of the lines (blue circle).






Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
y-5x=3 or y=5x+3
5x-2(5x+3)=-5
5x-10x-6=-5
-5x=-5+6
-5x=1
x=1/-5
x=-1/5 answer.
y=5*-1/5+3
y=-1+3
y=2 answer.
proof:
5*-1/5-2*2=-5
-1-4=-5
-5=-5