SOLUTION: Still having some problems with my homework. Can anyone help? 9x-2y=50 6x-2y=32 Thank you, Amanda

Algebra ->  Expressions-with-variables -> SOLUTION: Still having some problems with my homework. Can anyone help? 9x-2y=50 6x-2y=32 Thank you, Amanda      Log On


   

Question 153878: Still having some problems with my homework. Can anyone help?
9x-2y=50
6x-2y=32
Thank you,
Amanda
Found 2 solutions by jim_thompson5910, josmiceli:
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%289x-2y=50%2C6x-2y=32%29


-1%286x-2y%29=-1%2832%29 Multiply the both sides of the second equation by -1.


-6x%2B2y=-32 Distribute and multiply.


So we have the new system of equations:
system%289x-2y=50%2C-6x%2B2y=-32%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:


%289x-2y%29%2B%28-6x%2B2y%29=%2850%29%2B%28-32%29


%289x%2B-6x%29%2B%28-2y%2B2y%29=50%2B-32 Group like terms.


3x%2B0y=18 Combine like terms. Notice how the y terms cancel out.


3x=18 Simplify.


x=%2818%29%2F%283%29 Divide both sides by 3 to isolate x.


x=6 Reduce.


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


9x-2y=50 Now go back to the first equation.


9%286%29-2y=50 Plug in x=6.


54-2y=50 Multiply.


-2y=50-54 Subtract 54 from both sides.


-2y=-4 Combine like terms on the right side.


y=%28-4%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=2 Reduce.


So our answer is x=6 and y=2.


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 9x-2y=50 (red) and 6x-2y=32 (green)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You have 2 equations and 2 unknowns, so it's solvable
9x+-+2y+=+50
6x+-+2y+=+32
Multiply both sides of the 2nd equation by -1
9x+-+2y+=+50
-6x+%2B+2y+=+-32
Now add the equations
3x+=+18
x+=+6 answer
Substitute this value in the 1st equation
9x+-+2y+=+50
9%2A6+-+2y+=+50
54+-+2y+=+50
2y+=+54+-+50
2y+=+4
y+=+2 answer
------------------
check answers:
9x+-+2y+=+50
6x+-+2y+=+32
-----------------
9%2A6+-+2%2A2+=+50
54+-+4+=+50
50+=+50
OK
6%2A6+-+2%2A2+=+32
36+-+4+=+32
32+=+32
OK