SOLUTION: x+5y=10 -2x-10y=-20 5y=x+10 divide by 5, each side y=x+10/5 y=x/5+10/5 Problem with LCM I then plug y into next equation -2x-10(y equation)+ -10 (y equation)=-20 Need h

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: x+5y=10 -2x-10y=-20 5y=x+10 divide by 5, each side y=x+10/5 y=x/5+10/5 Problem with LCM I then plug y into next equation -2x-10(y equation)+ -10 (y equation)=-20 Need h      Log On


   

Question 126655This question is from textbook Beginning Algebra
: x+5y=10
-2x-10y=-20
5y=x+10
divide by 5, each side
y=x+10/5
y=x/5+10/5
Problem with LCM
I then plug y into next equation
-2x-10(y equation)+ -10 (y equation)=-20
Need help to make sense out of LCM to finish problem This question is from textbook Beginning Algebra

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%2B5y=10%2C-2x-10y=-20%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%2B5y=10 Start with the first equation


5y=10-x Subtract x from both sides


5y=-x%2B10 Rearrange the equation


y=%28-x%2B10%29%2F%285%29 Divide both sides by 5


y=%28%28-1%29%2F%285%29%29x%2B%2810%29%2F%285%29 Break up the fraction


y=%28-1%2F5%29x%2B2 Reduce



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

Since y=%28-1%2F5%29x%2B2, we can now replace each y in the second equation with %28-1%2F5%29x%2B2 to solve for x



-2x-10highlight%28%28%28-1%2F5%29x%2B2%29%29=-20 Plug in y=%28-1%2F5%29x%2B2 into the first equation. In other words, replace each y with %28-1%2F5%29x%2B2. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



-2x%2B%28-10%29%28-1%2F5%29x%2B%28-10%29%282%29=-20 Distribute -10 to %28-1%2F5%29x%2B2


-2x%2B%2810%2F5%29x-20=-20 Multiply


%285%29%28-2x%2B%2810%2F5%29x-20%29=%285%29%28-20%29 Multiply both sides by the LCM of 5. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



-10x%2B10x-100=-100 Distribute and multiply the LCM to each side



-100=-100 Combine like terms on the left side


0=-100%2B100Add 100 to both sides


0=0 Combine like terms on the right side




Since this equation is always true for any x value, this means x can equal any number. So there are an infinite number of solutions.