Which point is a solution to the system of inequalities graphed here?
\[
\begin{array}{l}
y \leq 2 x+2 \\
y \geq-5 x+4
\end{array}
\]
A. $(1,6)$
B. $(-6,0)$
C. $(0,5)$
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Step 1 ：We are given the system of inequalities \(y \leq 2x + 2\) and \(y \geq -5x + 4\). We are asked to find which of the given points is a solution to this system.

Step 2 ：We can do this by substituting the x and y values of each point into the inequalities and checking if the inequalities hold true.

Step 3 ：Let's start with point A, which is \((1, 6)\). Substituting these values into the inequalities, we get \(6 \leq 2(1) + 2\) and \(6 \geq -5(1) + 4\). Simplifying these inequalities, we get \(6 \leq 4\) and \(6 \geq -1\). The first inequality is not true, so point A is not a solution to the system of inequalities.

Step 4 ：Next, let's check point B, which is \((-6, 0)\). Substituting these values into the inequalities, we get \(0 \leq 2(-6) + 2\) and \(0 \geq -5(-6) + 4\). Simplifying these inequalities, we get \(0 \leq -10\) and \(0 \geq 34\). The first inequality is not true, so point B is not a solution to the system of inequalities.

Step 5 ：Finally, let's check point C, which is \((0, 5)\). Substituting these values into the inequalities, we get \(5 \leq 2(0) + 2\) and \(5 \geq -5(0) + 4\). Simplifying these inequalities, we get \(5 \leq 2\) and \(5 \geq 4\). The first inequality is not true, so point C is not a solution to the system of inequalities.

Step 6 ：None of the given points is a solution to the system of inequalities.