SOLUTION: need help with 7x/3 + 5y/4=4 5x/6 - 2y=21

Algebra ->  Systems-of-equations -> SOLUTION: need help with 7x/3 + 5y/4=4 5x/6 - 2y=21      Log On


   

Question 253103: need help with 7x/3 + 5y/4=4 5x/6 - 2y=21
Found 2 solutions by jim_thompson5910, richwmiller:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
7x%2F3%2B5y%2F4=4 Start with the first equation.


12%287x%2Fcross%283%29%2B5y%2Fcross%284%29%29=12%284%29 Multiply both sides by the LCD 12 to clear any fractions.


28x%2B15y=48 Distribute and multiply.


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

5x%2F6-2y=21 Move onto the second equation.


6%285x%2Fcross%286%29-2y%29=6%2821%29 Multiply both sides by the LCD 6 to clear any fractions.


5x-12y=126 Distribute and multiply.


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

So we now have the system of equations

system%2828x%2B15y=48%2C5x-12y=126%29


and it turns out that the solution to that system above is the same solution to the original system of equations.


Start with the given system of equations:
system%2828x%2B15y=48%2C5x-12y=126%29


4%2828x%2B15y%29=4%2848%29 Multiply the both sides of the first equation by 4.


112x%2B60y=192 Distribute and multiply.


5%285x-12y%29=5%28126%29 Multiply the both sides of the second equation by 5.


25x-60y=630 Distribute and multiply.


So we have the new system of equations:
system%28112x%2B60y=192%2C25x-60y=630%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:


%28112x%2B60y%29%2B%2825x-60y%29=%28192%29%2B%28630%29


%28112x%2B25x%29%2B%2860y%2B-60y%29=192%2B630 Group like terms.


137x%2B0y=822 Combine like terms.


137x=822 Simplify.


x=%28822%29%2F%28137%29 Divide both sides by 137 to isolate x.


x=6 Reduce.


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


112x%2B60y=192 Now go back to the first equation.


112%286%29%2B60y=192 Plug in x=6.


672%2B60y=192 Multiply.


60y=192-672 Subtract 672 from both sides.


60y=-480 Combine like terms on the right side.


y=%28-480%29%2F%2860%29 Divide both sides by 60 to isolate y.


y=-8 Reduce.


So the solutions are x=6 and y=-8.


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 28x%2B15y=48 (red) and 5x-12y=126 (green)

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Two lines that meet at (6,-8)
7x/3 + 5y/4=4
5x/6 - 2y=21
multiply the both of them by 6
14x+30y/4=24
5x-12y=126
multiply the first by 2
28x+15y=48
5x-12y=126
solve one of them for x in terms of y
5x=126+12y
x=126/5+12y/5
substitute that for x in the first
28*(126/5+12y/5)+15y=48
A little messy but it does come down to
y=-8
substitute -8 for y in either of the original