To determine whether the test point [tex]\((-1, 4)\)[/tex] is a solution to the linear inequality [tex]\(x + y \leq 1\)[/tex], we can follow these steps:
1. Substitute the values of the test point into the inequality:
The test point is [tex]\((x, y) = (-1, 4)\)[/tex]. We substitute -1 for [tex]\(x\)[/tex] and 4 for [tex]\(y\)[/tex] in the inequality [tex]\(x + y \leq 1\)[/tex].
2. Calculate the left-hand side of the inequality:
[tex]\[
x + y = -1 + 4 = 3
\][/tex]
3. Compare the calculated value to the right-hand side of the inequality:
The right-hand side of the inequality is 1. So, the inequality becomes:
[tex]\[
3 \leq 1
\][/tex]
4. Determine whether the inequality statement is true or false:
Since 3 is not less than or equal to 1, the statement [tex]\(3 \leq 1\)[/tex] is false.
Therefore, the test point [tex]\((-1, 4)\)[/tex] is not a solution to the inequality [tex]\(x + y \leq 1\)[/tex].
The correct choice is:
B. The test point [tex]\((-1,4)\)[/tex] is not a solution to the inequality because substituting [tex]\(-1\)[/tex] for [tex]\(x\)[/tex] and [tex]\(4\)[/tex] for [tex]\(y\)[/tex] makes the inequality a false statement.
