Answer
$(12,6)$ is a solution of the system
Work Step by Step
Equation 1: $2x - 3y = 6$
Equation 2: $x = 2y$
To determine whether $(12,6)$ is a solution of the system, we need to evaluate both equations using this point.
Equation 1:
$$2x - 3y = 6$$ $$2(12) - 3(6) = 6$$ $$24-18=6$$ $$6=6$$ $$TRUE$$
Equation 2:
$$x = 2y$$ $$12 = 2(6)$$ $$12=12$$ $$TRUE$$
Since both equations were satisfied, therefore $(12,6)$ is a solution of the system.