Question

question
determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
$x + 3y = -7$
$-2x - 6y = 11$
answer
\\(\circ\\) infinitely many solutions \\(\circ\\) no solutions
\\(\circ\\) one solution

Explanation:

Step1: Scale first equation

Multiply first equation by -2:
$$-2(x + 3y) = -2(-7)$$
$$-2x - 6y = 14$$

Step2: Compare to second equation

Compare scaled equation to $-2x -6y = 11$:
We get $14 = 11$, which is a false statement.

Answer:

No Solutions