SOLUTION: -4x-6y=7 x+5y=8

Algebra ->  Linear-equations -> SOLUTION: -4x-6y=7 x+5y=8      Log On


   

Question 127880: -4x-6y=7
x+5y=8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want to solve using substitution?






Start with the given system of equations:

system%28-4x-6y=7%2Cx%2B5y=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 first equation

-4x-6y=7 Start with the first equation


-6y=7%2B4x Add 4x to both sides


-6y=%2B4x%2B7 Rearrange the equation


y=%28%2B4x%2B7%29%2F%28-6%29 Divide both sides by -6


y=%28%28%2B4%29%2F%28-6%29%29x%2B%287%29%2F%28-6%29 Break up the fraction


y=%28-2%2F3%29x-7%2F6 Reduce



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

Since y=%28-2%2F3%29x-7%2F6, we can now replace each y in the second equation with %28-2%2F3%29x-7%2F6 to solve for x



x%2B5highlight%28%28%28-2%2F3%29x-7%2F6%29%29=8 Plug in y=%28-2%2F3%29x-7%2F6 into the first equation. In other words, replace each y with %28-2%2F3%29x-7%2F6. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x%2B%285%29%28-2%2F3%29x%2B%285%29%28-7%2F6%29=8 Distribute 5 to %28-2%2F3%29x-7%2F6


x-%2810%2F3%29x-35%2F6=8 Multiply


%286%29%281x-%2810%2F3%29x-35%2F6%29=%286%29%288%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-20x-35=48 Distribute and multiply the LCM to each side



-14x-35=48 Combine like terms on the left side


-14x=48%2B35Add 35 to both sides


-14x=83 Combine like terms on the right side


x=%2883%29%2F%28-14%29 Divide both sides by -14 to isolate x



x=-83%2F14 Reduce





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


So the first part of our answer is: x=-83%2F14









Since we know that x=-83%2F14 we can plug it into the equation y=%28-2%2F3%29x-7%2F6 (remember we previously solved for y in the first equation).



y=%28-2%2F3%29x-7%2F6 Start with the equation where y was previously isolated.


y=%28-2%2F3%29%28-83%2F14%29-7%2F6 Plug in x=-83%2F14


y=166%2F42-7%2F6 Multiply


y=39%2F14 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=39%2F14









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

So our answers are:

x=-83%2F14 and y=39%2F14

which form the point