We have to solve for x and y using the equations 1.5x-7y=2 and 0.625x+3y=-2.125

1.5x-7y=2

=> 3x - 14y = 4 ...(1)

0.625x+3y=-2.125

=> 5x + 24y = -17 ...(2)

Now 5*(1) - 3*(2)

=> 15x - 70y - 15x - 72y = 20 + 51

=> -144y = 71

=> y = -71 / 142

=> y = -1/2

substitute y = -1/2 in (1)

=> 3x - 14y = 4

=> 3x + 14/2 = 4

=> 3x = 4 - 7

=> 3x = -3

=> x = -3/3 = -1

**Therefore the required values of x and y are -1 and -1/2 respectively.**

We'll re-write the equations:

1.5x - 7y = 2

15x/10 - 7y = 2

3x/2 - 7y = 2

We'll multiply by 2:

3x - 14y = 4 (1)

0.625x+3y=-2.125.

625x/1000 + 3y = -2125/1000

We'll simplify the ratios by 25:

25x/40 + 3y = 85/40

We'll simplify the ratios by 5:

5x/8 + 3y = 17/8

5x + 24y = 17 (2)

We'll use determinats to solve the system:

det A = 3*24 - 5*(-14) = 72 + 70

det A = 142

Since det A is different from zero, the system has a determined solution.

x = det X/det A

142x = -14*17 - 24*(-14)

142x = -142

x = -1

3x - 14y = 4

-3 - 14y = 4

14y = -3-4

14y = -7

y = -7/14

**y = -1/2**