SOLUTION: Solve by the elimination method 0.3x-0.2y=4 0.5x+0.3y=5

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Question 145836: Solve by the elimination method

0.3x-0.2y=4
0.5x+0.3y=5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

0.3x-0.2y=4 Start with the first equation


10%280.3x-0.2y%29=10%284%29 Multiply both sides by 10 to move the decimal on each number 1 time. This will make every number a whole number.


3x-2y=40 Distribute and multiply

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0.5x%2B0.3y=5 Move onto the second equation


10%280.5x%2B0.3y%29=10%285%29 Multiply both sides by 10 to move the decimal on each number 1 time. This will make every number a whole number.


5x%2B3y=50 Distribute and multiply




So we now have the system of equations:

system%283x-2y=40%2C5x%2B3y=50%29



Now in order to solve this system by using elimination/addition, we need to solve (or isolate) one variable. I'm going to solve for y.





In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).


So lets eliminate x. In order to do that, we need to have both x coefficients that are equal in magnitude but have opposite signs (for instance 2 and -2 are equal in magnitude but have opposite signs). This way they will add to zero. By adding to zero, they can be eliminated.



So to make the x coefficients equal in magnitude but opposite in sign, we need to multiply both x coefficients by some number to get them to an common number. So if we wanted to get 3 and 5 to some equal number, we could try to get them to the LCM.



Since the LCM of 3 and 5 is 15, we need to multiply both sides of the top equation by 5 and multiply both sides of the bottom equation by -3 like this:




5%283x-2y%29=5%2840%29 Multiply the top equation (both sides) by 5
-3%285x%2B3y%29=-3%2850%29 Multiply the bottom equation (both sides) by -3




Distribute and multiply

15x-10y=200
-15x-9y=-150


Now add the equations together. In order to add 2 equations, group like terms and combine them

%2815x-15x%29%2B%28-10y-9y%29=200-150

Combine like terms and simplify



cross%2815x-15x%29-19y=50 Notice how the x terms cancel out




-19y=50 Simplify




y=50%2F-19 Divide both sides by -19 to isolate y




y=-50%2F19 Reduce



Now plug this answer into the top equation 3x-2y=40 to solve for x

3x-2y=40 Start with the first equation



3x-2%28-50%2F19%29=40 Plug in y=-50%2F19




3x%2B100%2F19=40 Multiply



%2819%29%283x%2B100%2F19%29=%2819%29%2840%29 Multiply both sides by the LCM of 19. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



57x%2B100=760 Distribute and multiply the LCM to each side



57x=760-100Subtract 100 from both sides


57x=660 Combine like terms on the right side


x=%28660%29%2F%2857%29 Divide both sides by 57 to isolate x



x=220%2F19 Reduce




So our answers are
x=220%2F19 and y=-50%2F19