SOLUTION: Solve the following equations for x and y or state that there is no solution. 5x – 3y = 5 x/2 + y/10 = 3

Algebra ->  Equations -> SOLUTION: Solve the following equations for x and y or state that there is no solution. 5x – 3y = 5 x/2 + y/10 = 3       Log On


   

Question 183047: Solve the following equations for x and y or state that
there is no solution.
5x – 3y = 5
x/2 + y/10 = 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
+x%2F2++%2B++y%2F10++=++3 Start with the second equation.


10%28x%2Fcross%282%29%29%2Bcross%2810%29%28y%2Fcross%2810%29%29=10%283%29 Multiply EVERY term by the LCD 10 to clear any fractions.


5x%2By=30 Distribute and multiply.


So we have the system of equations:


system%285x-3y=5%2C5x%2By=30%29



-1%285x%2By%29=-1%2830%29 Multiply the both sides of the second equation by -1.


-5x-y=-30 Distribute and multiply.


So we have the new system of equations:
system%285x-3y=5%2C-5x-y=-30%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:


%285x-3y%29%2B%28-5x-y%29=%285%29%2B%28-30%29


%285x-5x%29%2B%28-3y-y%29=5%2B-30 Group like terms.


0x-4y=-25 Combine like terms.


-4y=-25 Simplify.


y=%28-25%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=25%2F4 Reduce.


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


5x-3y=5 Now go back to the first equation.


5x-3%2825%2F4%29=5 Plug in y=25%2F4.


5x-75%2F4=5 Multiply.


4%285x%29-cross%284%29%2875%2Fcross%284%29%29=4%285%29 Multiply EVERY term by the LCD 4 to clear any fractions.


20x-75=20 Multiply.


20x=20%2B75 Add 75 to both sides.


20x=95 Combine like terms.


x=95%2F20 Divide both sides by 20 to isolate x.


x=19%2F4 Reduce.


So the solutions are x=19%2F4 and y=25%2F4


Which form the ordered pair .


This means that the system is consistent and independent.