SOLUTION: solve the equation for y 3/4 +5y=20 2/3x-1/2y=12

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Question 147154: solve the equation for y
3/4 +5y=20
2/3x-1/2y=12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%283%2F4%29x%2B5y=20 Start with the first equation.


4%28%283%2Fcross%284%29%29x%2B5y%29=4%2820%29 Multiply both sides by the LCD 4 to clear any fractions.


3x%2B20y=80 Distribute and multiply.


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%282%2F3%29x-%281%2F2%29y=12 Move onto the next equation.


6%28%282%2Fcross%283%29%29x-%281%2Fcross%282%29%29y%29=6%2812%29 Multiply both sides by the LCD 6 to clear any fractions.


4x-3y=72 Distribute and multiply.




So we have the given system of equations:
system%283x%2B20y=80%2C4x-3y=72%29


-4%283x%2B20y%29=-4%2880%29 Multiply the both sides of the first equation by -4.


-12x-80y=-320 Distribute and multiply.


3%284x-3y%29=3%2872%29 Multiply the both sides of the second equation by 3.


12x-9y=216 Distribute and multiply.


So we have the new system of equations:
system%28-12x-80y=-320%2C12x-9y=216%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:


%28-12x-80y%29%2B%2812x-9y%29=%28-320%29%2B%28216%29


%28-12x%2B12x%29%2B%28-80y%2B-9y%29=-320%2B216 Group like terms.


0x%2B-89y=-104 Combine like terms. Notice how the x terms cancel out.


-89y=-104 Simplify.


y=%28-104%29%2F%28-89%29 Divide both sides by -89 to isolate y.


y=104%2F89 Reduce.


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-12x-80y=-320 Now go back to the first equation.


-12x-80%28104%2F89%29=-320 Plug in y=104%2F89.


-12x-8320%2F89=-320 Multiply.


89%28-12x-8320%2Fcross%2889%29%29=89%28-320%29 Multiply both sides by the LCD 89 to clear any fractions.


-1068x-8320=-28480 Distribute and multiply.


-1068x=-28480%2B8320 Add 8320 to both sides.


-1068x=-20160 Combine like terms on the right side.


x=%28-20160%29%2F%28-1068%29 Divide both sides by -1068 to isolate x.


x=1680%2F89 Reduce.


So our answer is x=1680%2F89 and y=104%2F89.


Which form the ordered pair .


This means that the two equations are consistent and independent.