SOLUTION: 2x+4y=12 x +y= 4 answer: (2,2) i need a full break down on how my text book got 2,2 as a solution

Algebra ->  Systems-of-equations -> SOLUTION: 2x+4y=12 x +y= 4 answer: (2,2) i need a full break down on how my text book got 2,2 as a solution      Log On


   

Question 186755: 2x+4y=12
x +y= 4


answer: (2,2)

i need a full break down on how my text book got 2,2 as a solution
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=12%2Cx%2By=4%29


-2%28x%2By%29=-2%284%29 Multiply the both sides of the second equation by -2.


-2x-2y=-8 Distribute and multiply.


So we have the new system of equations:
system%282x%2B4y=12%2C-2x-2y=-8%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%28-2x-2y%29=%2812%29%2B%28-8%29


%282x%2B-2x%29%2B%284y%2B-2y%29=12%2B-8 Group like terms.


0x%2B2y=4 Combine like terms.


2y=4 Simplify.


y=%284%29%2F%282%29 Divide both sides by 2 to isolate y.


y=2 Reduce.


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


2x%2B4y=12 Now go back to the first equation.


2x%2B4%282%29=12 Plug in y=2.


2x%2B8=12 Multiply.


2x=12-8 Subtract 8 from both sides.


2x=4 Combine like terms on the right side.


x=%284%29%2F%282%29 Divide both sides by 2 to isolate x.


x=2 Reduce.


So the solutions are x=2 and y=2.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 2x%2B4y=12 (red) and x%2By=4 (green)