Physics Question, vector addition

Let a (vector)A+ b (vector)B+ (vector)C= 0, where (vector) A= (57, -5.9), (vector) B= (-54, 82) and (vector) C= (99,71).

What is the value of a and b?

a(57, -5.9) + b(-54, 82) + (99, 71) = (0, 0)

Consider x components only: 57a -54b + 99 = 0 (equation 1)
Consider y components only: -5.9a +82b + 71 = 0 (equation 2)

You then solve the 2 simultaneous equations. E.g.
Multiply equation 1 by 82/54: 86.56a - 82b + 150.33 = 0 (equation 3)
Add equations 2 and 3 : 80.66a + 221.33 = 0
a = -2.74
Then substitute a in equation 1, say, to find b.