Answer
FALSE
Work Step by Step
Equation 1: $2x - 3y = 5$
Equation 2: $6x + y = 1$
To determine whether $(1,-1)$ is a solution of the system, we need to evaluate both equations:
Equation 1: $$2x - 3y = 5$$ $$2(1) - 3(-1) = 5$$ $$2 + 3 = 5$$ $$5=5$$ $$TRUE$$
Equation 2: $$6x + y = 1$$ $$6(1) + (-1) = 1$$ $$6 -1 = 1$$ $$5=1$$ $$FALSE$$
Since only equation 1 was proved to be true after substituting the given point, therefore point $(1,-1)$ is not a solution of the system.