These examples will help you.
Consider the system of two equations (i) and (ii) underneath as:
2x - 3y = 8 ........ (i).
3x + 4y = -5 ........ (ii).
Step 1
Multiply (i) with 3
6x - 9y = 24 ...... (iii).
Multiply (ii) via 2
6x + 8y = - 10 ...... (iv).
Subtract iii from iv.
17y = -34 ......... (v).
y = -2
Step 2
Multiply (i) via 4
8x - 12y = 32 ....... (vi)
Multiply (ii) via 3
9x + 12y = -15 ..... (vii)
Add vi to vii
17x = 17 .......... (viii)
x = 1
Hence x = 1, y = -2 that is {1,-2}