SOLUTION: Solve the system by the addition (elimination) method. 2x+y=7 3x+y=12

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the system by the addition (elimination) method. 2x+y=7 3x+y=12      Log On


   

Question 187752This question is from textbook
: Solve the system by the addition (elimination) method.
2x+y=7
3x+y=12 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%282x%2By=7%2C3x%2By=12%29


-1%283x%2By%29=-1%2812%29 Multiply the both sides of the second equation by -1.


-3x-y=-12 Distribute and multiply.


So we have the new system of equations:
system%282x%2By=7%2C-3x-y=-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%2By%29%2B%28-3x-y%29=%287%29%2B%28-12%29


%282x-3x%29%2B%28y-y%29=7-12 Group like terms.


-x%2B0y=-5 Combine like terms.


-x=-5 Simplify.


x=%28-5%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=5 Reduce.


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2x%2By=7 Now go back to the first equation.


2%285%29%2By=7 Plug in x=5.


10%2By=7 Multiply.


y=7-10 Subtract 10 from both sides.


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


So the solutions are x=5 and y=-3.


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%2By=7 (red) and 3x%2By=12 (green)