SOLUTION: 1000x+30y=500 x-2y=11

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Question 124486: 1000x+30y=500
x-2y=11
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Do you want to solve by substitution?


Start with the given system of equations:

system%281000x%2B30y=500%2Cx-2y=11%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

1000x%2B30y=500 Start with the first equation


30y=500-1000x Subtract 1000x from both sides


30y=-1000x%2B500 Rearrange the equation


y=%28-1000x%2B500%29%2F%2830%29 Divide both sides by 30


y=%28%28-1000%29%2F%2830%29%29x%2B%28500%29%2F%2830%29 Break up the fraction


y=%28-100%2F3%29x%2B50%2F3 Reduce



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

Since y=%28-100%2F3%29x%2B50%2F3, we can now replace each y in the second equation with %28-100%2F3%29x%2B50%2F3 to solve for x



x-2highlight%28%28%28-100%2F3%29x%2B50%2F3%29%29=11 Plug in y=%28-100%2F3%29x%2B50%2F3 into the first equation. In other words, replace each y with %28-100%2F3%29x%2B50%2F3. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x%2B%28-2%29%28-100%2F3%29x%2B%28-2%29%2850%2F3%29=11 Distribute -2 to %28-100%2F3%29x%2B50%2F3


x%2B%28200%2F3%29x-100%2F3=11 Multiply


%283%29%281x%2B%28200%2F3%29x-100%2F3%29=%283%29%2811%29 Multiply both sides by the LCM of 3. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



3x%2B200x-100=33 Distribute and multiply the LCM to each side



203x-100=33 Combine like terms on the left side


203x=33%2B100Add 100 to both sides


203x=133 Combine like terms on the right side


x=%28133%29%2F%28203%29 Divide both sides by 203 to isolate x



x=19%2F29 Reduce





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


So the first part of our answer is: x=19%2F29









Since we know that x=19%2F29 we can plug it into the equation y=%28-100%2F3%29x%2B50%2F3 (remember we previously solved for y in the first equation).



y=%28-100%2F3%29x%2B50%2F3 Start with the equation where y was previously isolated.


y=%28-100%2F3%29%2819%2F29%29%2B50%2F3 Plug in x=19%2F29


y=-1900%2F87%2B50%2F3 Multiply


y=-150%2F29 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=-150%2F29









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

So our answers are:

x=19%2F29 and y=-150%2F29

which form the point