SOLUTION: Solve by the elimination method 4x-9y=14.5 7y-2x=-8.5

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Question 145837: Solve by the elimination method

4x-9y=14.5
7y-2x=-8.5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4x-9y=14.5 Start with the first equation


10%284x-9y%29=10%2814.5%29 Multiply both sides by 10 to move the decimal on each number 1 time. This will make every number a whole number.


40x-90y=145 Distribute and multiply


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7y-2x=-8.5 Start with the second equation


10%287y-2x%29=10%28-8.5%29 Multiply both sides by 10 to move the decimal on each number 1 time. This will make every number a whole number.


70y-20x=-85 Distribute and multiply


-20x%2B70y=-85 Rearrange the x and y terms



So we now have the system of equations:

system%2840x-90y=145%2C-20x%2B70y=-85%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 40 and -20 to some equal number, we could try to get them to the LCM.



Since the LCM of 40 and -20 is 40, we need to multiply both sides of the top equation by 1 and multiply both sides of the bottom equation by 2 like this:




1%2840x-90y%29=1%28145%29 Multiply the top equation (both sides) by 1
2%28-20x%2B70y%29=2%28-85%29 Multiply the bottom equation (both sides) by 2




Distribute and multiply

40x-90y=145
-40x%2B140y=-170


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

%2840x-40x%29%2B%28-90y%2B140y%29=145-170

Combine like terms and simplify



cross%2840x-40x%29%2B50y=-25 Notice how the x terms cancel out




50y=-25 Simplify




y=-25%2F50 Divide both sides by 50 to isolate y




y=-1%2F2 Reduce



Now plug this answer into the top equation 40x-90y=145 to solve for x

40x-90y=145 Start with the first equation



40x-90%28-1%2F2%29=145 Plug in y=-1%2F2




40x%2B90%2F2=145 Multiply




40x%2B45=145 Reduce



40x=145-45Subtract 45 from both sides


40x=100 Combine like terms on the right side


x=%28100%29%2F%2840%29 Divide both sides by 40 to isolate x



x=5%2F2 Reduce




So our answer is
x=5%2F2 and y=-1%2F2



which also looks like