SOLUTION: I need to solve the following problems using substitution. Do I need to get the y on one side by itself in order to solve the problem or can I use the x by itself on one side and u

Algebra ->  Linear-equations -> SOLUTION: I need to solve the following problems using substitution. Do I need to get the y on one side by itself in order to solve the problem or can I use the x by itself on one side and u      Log On


   

Question 127891: I need to solve the following problems using substitution. Do I need to get the y on one side by itself in order to solve the problem or can I use the x by itself on one side and use substitution. Can the problem be -x=-2y+1 or does the x need to be positive before i can substitute it in the other equation. Im sorry if it sounds so confusing but Im a little confused. Thank you.
x-3y=9
-x+2y=1
If you have time would you be able to show me an example of elimination also. If not I understand. Thank you for your time.
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%28x-3y=9%2C-x%2B2y=1%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-3y=9 Start with the first equation


-3y=9-x Subtract x from both sides


-3y=-x%2B9 Rearrange the equation


y=%28-x%2B9%29%2F%28-3%29 Divide both sides by -3


y=%28%28-1%29%2F%28-3%29%29x%2B%289%29%2F%28-3%29 Break up the fraction


y=%281%2F3%29x-3 Reduce



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

Since y=%281%2F3%29x-3, we can now replace each y in the second equation with %281%2F3%29x-3 to solve for x



-x%2B2highlight%28%28%281%2F3%29x-3%29%29=1 Plug in y=%281%2F3%29x-3 into the first equation. In other words, replace each y with %281%2F3%29x-3. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



-x%2B%282%29%281%2F3%29x%2B%282%29%28-3%29=1 Distribute 2 to %281%2F3%29x-3


-x%2B%282%2F3%29x-6=1 Multiply


%283%29%28-1x%2B%282%2F3%29x-6%29=%283%29%281%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%2B2x-18=3 Distribute and multiply the LCM to each side



-x-18=3 Combine like terms on the left side


-x=3%2B18Add 18 to both sides


-x=21 Combine like terms on the right side


x=%2821%29%2F%28-1%29 Divide both sides by -1 to isolate x



x=-21 Divide





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


So the first part of our answer is: x=-21









Since we know that x=-21 we can plug it into the equation y=%281%2F3%29x-3 (remember we previously solved for y in the first equation).



y=%281%2F3%29x-3 Start with the equation where y was previously isolated.


y=%281%2F3%29%28-21%29-3 Plug in x=-21


y=-21%2F3-3 Multiply


y=-10 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=-10









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

So our answers are:

x=-21 and y=-10

which form the point