Please help solve this using L.C.M and explain the steps plz ty.

9514 1404 393

  (x, y) = (2, 3)

Step-by-step explanation:

The first step is to find the least common multiple of the denominators of each of the equations. If the denominators have no common factors, a reasonable choice is their product. Here, it works to start with the fractions that must be added, then compare the LCM found to the denominator on the right to see if any further factors must be included.

First equation:

  LCM = 3×4 = 12

  12(2x/3 -y/4) = 12(7/12) . . . . . multiply the equation by 12

 8x -3y = 7 . . . . . . . . . simplify

Second equation:

  LCM = 4×5 =20

  20(3x/4 -2y/5) = 20(3/10) . . . . multiply equation by 20

  15x -8y = 6 . . . . . . simplify

Solve by elimination

We can eliminate the y-variable by subtracting 3 times the second equation from 8 times the first:

  8(8x -3y) -3(15x -8y) = 8(7) -3(6)

  19x = 38 . . . . . simplify

  x = 2 . . . . . . . divide by 19

Substituting into the first equation gives ...

  8(2) -3y = 7

  3y = 9 . . . . . . add 3y-7

  y = 3 . . . . . divide by 3

The solution is ...

  (x, y) = (2, 3)

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There are many ways to solve such a system of equations. Using the LCM to eliminate fractions is one way to start. You can also do the arithmetic with the fractions intact, though most folks don't care to. In addition to the elimination method used here, you can use matrix or graphical methods, substitution, or any of the variations of Cramer's Rule.