# SOLUTION: I am having trouble understanding system of equations. i have tried to work the problem out but im not sure what steps to take. can you help me on the problem 3x/2 + y/4=7 x/5 - 2

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 Click here to see ALL problems on Linear-systems Question 54398: I am having trouble understanding system of equations. i have tried to work the problem out but im not sure what steps to take. can you help me on the problem 3x/2 + y/4=7 x/5 - 2y/3 = 2 1/3Found 3 solutions by Edwin McCravy, stanbon, Earlsdon:Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!```I am having trouble understanding system of equations. i have tried to work the problem out but im not sure what steps to take. can you help me on the problem 3x/2 + y/4 = 7 x/5 - 2y/3 = 2 1/3 We need to clear fractions in each equation: Put the the 7 of the first equation over 1 so everything will be a fraction: 3x y 7 ---- + --- = --- 2 4 1 Multiply every term by the LCD of 3 and 4, which is 12. Put it over 1 too: 12 3x 12 y 12 7 ----·---- + ----·--- = ----·--- 1 2 1 4 1 1 Cancel the 2 into the 12 in the first term, getting 6. Cancel the 4 into the 12 in the second term, getting 3. 6 3 12 3x 12 y 12 7 ----·---- + ----·--- = ----·--- 1 2 1 4 1 1 1 1 All that's left is 18x + 3y = 84 ------------------------ x/5 - 2y/3 = 2 1/3 Change the 2 1/3 to a mixed fraction 7/3 x/5 - 2y/3 = 2 1/3 x 2y 7 --- - ---- = --- 5 3 3 Multiply every term by the LCD of 5, 3 and 3, which is 15. Put it over 1 too: 15 x 15 2y 15 7 ----·--- - ----·---- = ----·--- 1 5 1 3 1 3 Cancel the 5 into the 15 in the first term, getting 3. Cancel the 3 into the 15 in the second term, getting 5. Cancel the 3 into the 15 in the term on the right, getting 5 3 5 5 15 x 15 2y 15 7 ----·--- - ----·---- = ----·--- 1 5 1 3 1 3 1 1 1 All that's left is 3x - 10y = 35 ----------------------------------------------- Now you have the fractionless system 18x + 3y = 84 3x - 10y = 35 Can you solve that system? If not post again. Answer: (x, y) = (5, 2) Edwin``` Answer by stanbon(57352)   (Show Source): You can put this solution on YOUR website!1st:3x/2 + y/4=7 Multiply thru by 4 to get: 2nd: 6x+y=28 3rd: x/5 - 2y/3 = 2 1/3 Multiply thru by 15 to get: 4th: 3x-19y=35 To eliminate the "x" terms multiply thru 4th by 2 to get: 5th: 6x-38y=70 Subtract 5th from 2nd to get: 6th: 39y=-42 Then y=-14/13 Substitute that into 2nd to solve for "x": 6x-14/13 = 28 6x=14/13 + 364/13 6x = 378/13 x= 63/13 Solution: x=63/13 y=-14/13 cheers, Stan H. Answer by Earlsdon(6287)   (Show Source): You can put this solution on YOUR website!Solve the system of equations: 1) Multiply through by 4, the LCD to clear the fractions. 1a) 2) Mulitiply through by 15, the LCD to clear the fractions. 2a) Rewrite equation 1a) as: 1b) and substitute for y in equation 2a) 2b) Simplify and solve for x. 2c) 2d) Divide both sides by 63. 2e) Now substitute this for x in equation 1b) 1c) 1d) The solution to the system of equations is: (5, -2)