SOLUTION: solve the system of equations 4x + 5y = -41 3x - 2y = 21

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Question 222939: solve the system of equations
4x + 5y = -41
3x - 2y = 21
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%284x%2B5y=-41%2C3x-2y=21%29


2%284x%2B5y%29=2%28-41%29 Multiply the both sides of the first equation by 2.


8x%2B10y=-82 Distribute and multiply.


5%283x-2y%29=5%2821%29 Multiply the both sides of the second equation by 5.


15x-10y=105 Distribute and multiply.


So we have the new system of equations:
system%288x%2B10y=-82%2C15x-10y=105%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:


%288x%2B10y%29%2B%2815x-10y%29=%28-82%29%2B%28105%29


%288x%2B15x%29%2B%2810y%2B-10y%29=-82%2B105 Group like terms.


23x%2B0y=23 Combine like terms. Notice how the y terms cancel out.


23x=23 Simplify.


x=%2823%29%2F%2823%29 Divide both sides by 23 to isolate x.


x=1 Reduce.


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


8x%2B10y=-82 Now go back to the first equation.


8%281%29%2B10y=-82 Plug in x=1.


8%2B10y=-82 Multiply.


10y=-82-8 Subtract 8 from both sides.


10y=-90 Combine like terms on the right side.


y=%28-90%29%2F%2810%29 Divide both sides by 10 to isolate y.


y=-9 Reduce.


So our answer is x=1 and y=-9.


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 4x%2B5y=-41 (red) and 3x-2y=21 (green)