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Junior high school mathematics substitution method
3x+4y= 10 ①

5x-6y=33 ②

①×5 -②×3:

15x+20y- 15x+ 18y = 50-99

38y=-49

y=-49/38

Substitute y=-49/38 into ① to get:

3x+ 4(-49/38)= 10

3x - 98/ 19 = 10

3x=98/ 19 + 10

3x=288/ 19

x= 96/ 19

So x=96/ 19 y=-49/38 is the solution of the original equation.