SOLUTION: Hello there. I need help on a problem. It says Use elimination to solve each system of equations. Heres the question. x+y= 14 x-y= 20 I did this x-y=14 x+y=20 I j

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Hello there. I need help on a problem. It says Use elimination to solve each system of equations. Heres the question. x+y= 14 x-y= 20 I did this x-y=14 x+y=20 I j      Log On


   

Question 322469: Hello there. I need help on a problem. It says Use elimination to solve each system of equations.
Heres the question.
x+y= 14
x-y= 20
I did this x-y=14
x+y=20 I just basically got y=6 but it says its the wrong answer and i really dont know how to get the answer. If you know can you please show me step by step so i can better understand Algebra. Iv been taking this course for 2yrs and i failed it. This is my third atempt. Thank you.
Found 2 solutions by jim_thompson5910, solver91311:
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%2By=14%2Cx-y=20%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28x%2By%29%2B%28x-y%29=%2814%29%2B%2820%29


%28x%2Bx%29%2B%28y-y%29=14%2B20 Group like terms.


2x%2B0y=34 Combine like terms.


2x=34 Simplify.


x=%2834%29%2F%282%29 Divide both sides by 2 to isolate x.


x=17 Reduce.


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


x%2By=14 Now go back to the first equation.


17%2By=14 Plug in x=17.


y=14-17 Subtract 17 from both sides.


y=-3 Combine like terms on the right side.


So the solutions are x=17 and y=-3.


Which form the ordered pair .


This means that the system is consistent and independent.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The idea of solving a linear system by elimination is to multiply one or more of the given equations by a constant or constants so that the coefficients on one of the variables are additive inverses in two of the equations.

For the example problem, this first step is unnecessary because you already have the coefficients on as additive inverses, namely 1 and -1.

Now you need to add the equations, term by term:





, , and , hence:







Now that you know the value of , substitute it back into either of the original equations:





And there you have it. The solution set is the ordered pair

John