To determine if the point [tex]\((1, -1)\)[/tex] is a solution to the given system of inequalities, we need to check if this point satisfies both inequalities.
Step 1: Check the first inequality [tex]\(2x + y < 4\)[/tex]
Substitute [tex]\(x = 1\)[/tex] and [tex]\(y = -1\)[/tex] into the inequality:
[tex]\[ 2(1) + (-1) < 4 \][/tex]
[tex]\[ 2 - 1 < 4 \][/tex]
[tex]\[ 1 < 4 \][/tex]
This statement is true.
Step 2: Check the second inequality [tex]\(-2x + y \leq 4\)[/tex]
Substitute [tex]\(x = 1\)[/tex] and [tex]\(y = -1\)[/tex] into the inequality:
[tex]\[ -2(1) + (-1) \leq 4 \][/tex]
[tex]\[ -2 - 1 \leq 4 \][/tex]
[tex]\[ -3 \leq 4 \][/tex]
This statement is also true.
Since both inequalities are satisfied, the point [tex]\((1, -1)\)[/tex] is a solution to the system:
[tex]\[
\begin{array}{l}
2x + y < 4 \\
-2x + y \leq 4
\end{array}
\][/tex]
Therefore, the answer is:
True
