Question

determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
\\(-4x + 5y = -1\\)
\\(-12x + 15y = 6\\)
answer
one solution
infinitely many solutions
no solutions

Explanation:

Step1: Scale first equation by 3

Multiply $-4x + 5y = -1$ by 3:
$$3(-4x + 5y) = 3(-1)$$
$$-12x + 15y = -3$$

Step2: Compare to second equation

Second equation: $-12x + 15y = 6$
We have $-12x + 15y = -3$ and $-12x + 15y = 6$, which are contradictory (same left side, different right sides).

Answer:

No Solutions