SOLUTION: I am needing to solve this equation by the addition (elimination method) 2x+4y=8 7x+2y=10 Can you help me?

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: I am needing to solve this equation by the addition (elimination method) 2x+4y=8 7x+2y=10 Can you help me?      Log On


   

Question 166125: I am needing to solve this equation by the addition (elimination method)
2x+4y=8
7x+2y=10
Can you help me?
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%282x%2B4y=8%2C7x%2B2y=10%29


-2%287x%2B2y%29=-2%2810%29 Multiply the both sides of the second equation by -2.


-14x-4y=-20 Distribute and multiply.


So we have the new system of equations:
system%282x%2B4y=8%2C-14x-4y=-20%29


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


%282x%2B4y%29%2B%28-14x-4y%29=%288%29%2B%28-20%29


%282x%2B-14x%29%2B%284y%2B-4y%29=8%2B-20 Group like terms.


-12x%2B0y=-12 Combine like terms. Notice how the y terms cancel out.


-12x=-12 Simplify.


x=%28-12%29%2F%28-12%29 Divide both sides by -12 to isolate x.


x=1 Reduce.


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


2x%2B4y=8 Now go back to the first equation.


2%281%29%2B4y=8 Plug in x=1.


2%2B4y=8 Multiply.


4y=8-2 Subtract 2 from both sides.


4y=6 Combine like terms on the right side.


y=%286%29%2F%284%29 Divide both sides by 4 to isolate y.


y=3%2F2 Reduce.


So our answer is x=1 and y=3%2F2.


Which form the ordered pair .


This means that the system is consistent and independent.