We have to solve

1.5x - 7y = 2 ...(1)

0.625x + 3y = -2.125 ...(2)

3*(1) + 7*(2)

=> 4.5x - 21y + 4.375x + 21y = 6 - 14.875

=> 8.875x = -8.875

=> x = -1

Substitute in (1)

-1.5 - 7y = 2

=> -7y = 3.5

=> y = -1/2

**The solution is x = -1 and y = -1/2**

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