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

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) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

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

Start with the first equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

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

Since , we can now replace each in the second equation with to solve for

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

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)

Distribute and multiply the LCM to each side

Combine like terms on the left side

Add 100 to both sides

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.

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