SOLUTION: solve each system of linear equations by addition or elimination 1) 3x + y = 7 4x + 2y = 16

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: solve each system of linear equations by addition or elimination 1) 3x + y = 7 4x + 2y = 16      Log On


   

Question 241743: solve each system of linear equations by addition or elimination


1) 3x + y = 7
4x + 2y = 16
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%283x%2By=7%2C4x%2B2y=16%29


-2%283x%2By%29=-2%287%29 Multiply the both sides of the first equation by -2.


-6x-2y=-14 Distribute and multiply.


So we have the new system of equations:
system%28-6x-2y=-14%2C4x%2B2y=16%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:


%28-6x-2y%29%2B%284x%2B2y%29=%28-14%29%2B%2816%29


%28-6x%2B4x%29%2B%28-2y%2B2y%29=-14%2B16 Group like terms.


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


-2x=2 Simplify.


x=%282%29%2F%28-2%29 Divide both sides by -2 to isolate x.


x=-1 Reduce.


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


-6x-2y=-14 Now go back to the first equation.


-6%28-1%29-2y=-14 Plug in x=-1.


6-2y=-14 Multiply.


-2y=-14-6 Subtract 6 from both sides.


-2y=-20 Combine like terms on the right side.


y=%28-20%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=10 Reduce.


So the solutions are x=-1 and y=10.


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 3x%2By=7 (red) and 4x%2B2y=16 (green)