SOLUTION: 2x-6y=5 x+y=2 solve the system of equations

Algebra ->  Linear-equations -> SOLUTION: 2x-6y=5 x+y=2 solve the system of equations       Log On


   

Question 678297: 2x-6y=5
x+y=2
solve the system of equations

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm going to use elimination.



Start with the given system of equations:
system%282x-6y=5%2Cx%2By=2%29


6%28x%2By%29=6%282%29 Multiply the both sides of the second equation by 6.


6x%2B6y=12 Distribute and multiply.


So we have the new system of equations:
system%282x-6y=5%2C6x%2B6y=12%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-6y%29%2B%286x%2B6y%29=%285%29%2B%2812%29


%282x%2B6x%29%2B%28-6y%2B6y%29=5%2B12 Group like terms.


8x%2B0y=17 Combine like terms.


8x=17 Simplify.


x=%2817%29%2F%288%29 Divide both sides by 8 to isolate x.


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


2x-6y=5 Now go back to the first equation.


2%2817%2F8%29-6y=5 Plug in x=17%2F8.


17%2F4-6y=5 Multiply.


4%2817%2Fcross%284%29-6y%29=4%285%29 Multiply both sides by the LCD 4 to clear any fractions.


17-24y=20 Distribute and multiply.


-24y=20-17 Subtract 17 from both sides.


-24y=3 Combine like terms on the right side.


y=%283%29%2F%28-24%29 Divide both sides by -24 to isolate y.


y=-1%2F8 Reduce.


So the solutions are x=17%2F8 and y=-1%2F8.


Which form the ordered pair .


This means that the system is consistent and independent.