SOLUTION: 4x+6y=15 -x+2y=5

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Question 127285: 4x+6y=15
-x+2y=5
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%284x%2B6y=15%2C-x%2B2y=5%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

4x%2B6y=15 Start with the first equation


6y=15-4x Subtract 4x from both sides


6y=-4x%2B15 Rearrange the equation


y=%28-4x%2B15%29%2F%286%29 Divide both sides by 6


y=%28%28-4%29%2F%286%29%29x%2B%2815%29%2F%286%29 Break up the fraction


y=%28-2%2F3%29x%2B5%2F2 Reduce



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

Since y=%28-2%2F3%29x%2B5%2F2, we can now replace each y in the second equation with %28-2%2F3%29x%2B5%2F2 to solve for x



-x%2B2highlight%28%28%28-2%2F3%29x%2B5%2F2%29%29=5 Plug in y=%28-2%2F3%29x%2B5%2F2 into the first equation. In other words, replace each y with %28-2%2F3%29x%2B5%2F2. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



-x%2B%282%29%28-2%2F3%29x%2B%282%29%285%2F2%29=5 Distribute 2 to %28-2%2F3%29x%2B5%2F2


-x-%284%2F3%29x%2B10%2F2=5 Multiply


%286%29%28-1x-%284%2F3%29x%2B10%2F2%29=%286%29%285%29 Multiply both sides by the LCM of 6. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



-6x-8x%2B30=30 Distribute and multiply the LCM to each side



-14x%2B30=30 Combine like terms on the left side


-14x=30-30Subtract 30 from both sides


-14x=0 Combine like terms on the right side


x=%280%29%2F%28-14%29 Divide both sides by -14 to isolate x



x=0 Divide





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


So the first part of our answer is: x=0









Since we know that x=0 we can plug it into the equation y=%28-2%2F3%29x%2B5%2F2 (remember we previously solved for y in the first equation).



y=%28-2%2F3%29x%2B5%2F2 Start with the equation where y was previously isolated.


y=%28-2%2F3%29%280%29%2B5%2F2 Plug in x=0


y=0%2F3%2B5%2F2 Multiply


y=5%2F2 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=5%2F2









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

So our answers are:

x=0 and y=5%2F2

which form the point