SOLUTION: hi, i need to solve this using elimination method and check 15x+3y=-12 2x+y=8

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: hi, i need to solve this using elimination method and check 15x+3y=-12 2x+y=8      Log On


   

Question 147695This question is from textbook
: hi, i need to solve this using elimination method and check
15x+3y=-12
2x+y=8 This question is from textbook

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%2815x%2B3y=-12%2C2x%2By=8%29


-3%282x%2By%29=-3%288%29 Multiply the both sides of the second equation by -3.


-6x-3y=-24 Distribute and multiply.


So we have the new system of equations:
system%2815x%2B3y=-12%2C-6x-3y=-24%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:


%2815x%2B3y%29%2B%28-6x-3y%29=%28-12%29%2B%28-24%29


%2815x%2B-6x%29%2B%283y%2B-3y%29=-12%2B-24 Group like terms.


9x%2B0y=-36 Combine like terms. Notice how the y terms cancel out.


9x=-36 Simplify.


x=%28-36%29%2F%289%29 Divide both sides by 9 to isolate x.


x=-4 Reduce.


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


15x%2B3y=-12 Now go back to the first equation.


15%28-4%29%2B3y=-12 Plug in x=-4.


-60%2B3y=-12 Multiply.


3y=-12%2B60 Add 60 to both sides.


3y=48 Combine like terms on the right side.


y=%2848%29%2F%283%29 Divide both sides by 3 to isolate y.


y=16 Reduce.


So our answer is x=-4 and y=16.


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 15x%2B3y=-12 (red) and 2x%2By=8 (green)


---------------------------
Check:



15x%2B3y=-12 Start with the first equation.


15%2A%28-4%29%2B3%2A%2816%29=-12 Plug in x=-4 and y=16.


-12=-12 Evaluate and simplify the left side.


Since the equation is true, this means that (-4,16) is a solution of the first equation


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


2x%2By=8 Start with the second equation.


2%2A%28-4%29%2B%2816%29=8 Plug in x=-4 and y=16.


8=8 Evaluate and simplify the left side.


Since the equation is true, this means that (-4,16) is a solution of the second equation.


Since all of the equations of the system are true, this means that (-4,16) is a solution to the system. So this verifies our answer.