SOLUTION: Multiply both side of the equation by a common denominator to eliminate the fractions. Then solve the system. x/5+3y=31 2x-y/5=8 I have been struggling to try to solve th

Algebra ->  Matrices-and-determiminant -> SOLUTION: Multiply both side of the equation by a common denominator to eliminate the fractions. Then solve the system. x/5+3y=31 2x-y/5=8 I have been struggling to try to solve th      Log On


   

Question 332786: Multiply both side of the equation by a common denominator to eliminate the
fractions. Then solve the system.
x/5+3y=31
2x-y/5=8
I have been struggling to try to solve this for over 4 days now and have had no
luck. We are given the final answer which is (5,10) but I can not figurge out
how they got to that. I need to show the work and solve the problem. Can
someone please help me.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
1) x%2F5+%2B+3y+=+31
2) 2x-y%2F5+=+8 First multiply both sides of both equations by 5 to clear the fractons.
1a) 5%28x%2F5+%2B+3y%29+=+5%2831%29
1b) x%2B15y+=+155
2a) 5%282x-y%2F5%29+=+5%288%29
2b) 10x-y+=+40
Now you have a choice here. You want to get both equations to have the number of either the x-variable or the y-variable so that you can subtract (or add) the two equation to eliminate that variable. I chose to multiply equation 1b) by 10 so that I can eliminate the x-variable by subtracting.
1c) 10x%2B150y+=+1550
2b) 10x-y+=+40 Subtract equation 2b) from equation 1c) which eliminates the x-variable.
3) 151y+=+1510 Now divide both sides by 151.
3a) highlight%28y+=+10%29 Now substitute this into equation 1) or 2) to solve for x. I chose equation 2).
2x-y%2F5+=+8 Substitute y = 10.
2x-10%2F5+=+8 Simplify.
2x-2+=+8 Add 2 to both sides.
2x+=+10 Divide both sides by 2.
highlight%28x+=+5%29
The answer is: (5, 10)