SOLUTION: Hi need help please in solving all values of x and y and can you please show me each step 1. 5x + 2y =16 3x - 5y =-9

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Question 188361: Hi need help please in solving all values of x and y and can you please show me each step
1. 5x + 2y =16
3x - 5y =-9



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%285x%2B2y=16%2C3x-5y=-9%29


5%285x%2B2y%29=5%2816%29 Multiply the both sides of the first equation by 5.


25x%2B10y=80 Distribute and multiply.


2%283x-5y%29=2%28-9%29 Multiply the both sides of the second equation by 2.


6x-10y=-18 Distribute and multiply.


So we have the new system of equations:
system%2825x%2B10y=80%2C6x-10y=-18%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:


%2825x%2B10y%29%2B%286x-10y%29=%2880%29%2B%28-18%29


%2825x%2B6x%29%2B%2810y%2B-10y%29=80%2B-18 Group like terms.


31x%2B0y=62 Combine like terms.


31x=62 Simplify.


x=%2862%29%2F%2831%29 Divide both sides by 31 to isolate x.


x=2 Reduce.


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


25x%2B10y=80 Now go back to the first equation.


25%282%29%2B10y=80 Plug in x=2.


50%2B10y=80 Multiply.


10y=80-50 Subtract 50 from both sides.


10y=30 Combine like terms on the right side.


y=%2830%29%2F%2810%29 Divide both sides by 10 to isolate y.


y=3 Reduce.


So the solutions are x=2 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 5x%2B2y=16 (red) and 3x-5y=-9 (green)