Is $$ (3,-2) $$ a solution to this system of equations? $$ \begin{array}{l}y=\frac{1}{3} x+1 \ y=2 x+2\end{array} $$ yes no

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To determine if the point $$ (3, -2) $$ is a solution to the system of equations, we need to substitute $$ x = 3 $$ and $$ y = -2 $$ into both equations and check if both equations are satisfied.

1. For the first equation $$ y = \frac{1}{3} x + 1 $$:
   $$
   y = \frac{1}{3}(3) + 1 = 1 + 1 = 2
   $$
   Here, $$ y $$ should equal $$ -2 $$, but we found $$ y = 2 $$. So, the first equation is not satisfied.

2. For the second equation $$ y = 2x + 2 $$:
   $$
   y = 2(3) + 2 = 6 + 2 = 8
   $$
   Again, $$ y $$ should equal $$ -2 $$, but we found $$ y = 8 $$. So, the second equation is also not satisfied.

Since the point $$ (3, -2) $$ does not satisfy either equation, the answer is **no**.
The point $$ (3, -2) $$ is not a solution to the system of equations.

Is a solution to this system of equations?

yes no

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Is a solution to this system of equations? yes no