Question

How many solutions does the system have?
12x−15y=18
12
𝑥
−
15
𝑦
=
18

4x−5y=6
4
𝑥
−
5
𝑦
=
6

Answer 1

Infinitely many. The two equations are equivalent (multiply 4x − 5y = 6 by 3 to get 12x − 15y = 18), so they represent the same line. All points satisfying 4x − 5y = 6 are solutions, e.g. y = (4x − 6)/5 for any real x.