Question

which of the following points does not lie in the solution set of the system of inequalities below?
$2x - 5y \leq 15$
$4x + y \leq -4$
\bigcirc (-5, 1)
\bigcirc (-2, -5)
\bigcirc (-8, 0)
\bigcirc (-3, -3)

Explanation:

Step1: Test point (-5,1)

Substitute \(x = -5\), \(y = 1\) into \(2x - 5y \leq 15\):
\(2(-5) - 5(1) = -10 - 5 = -15 \leq 15\) (true).
Substitute into \(4x + y \leq -4\):
\(4(-5) + 1 = -20 + 1 = -19 \leq -4\) (true).

Step2: Test point (-2,-5)

Substitute \(x = -2\), \(y = -5\) into \(2x - 5y \leq 15\):
\(2(-2) - 5(-5) = -4 + 25 = 21
leq 15\) (false).
(We can stop here, but check others for confirmation.)

Step3: Test point (-8,0)

Substitute \(x = -8\), \(y = 0\) into \(2x - 5y \leq 15\):
\(2(-8) - 5(0) = -16 \leq 15\) (true).
Substitute into \(4x + y \leq -4\):
\(4(-8) + 0 = -32 \leq -4\) (true).

Step4: Test point (-3,-3)

Substitute \(x = -3\), \(y = -3\) into \(2x - 5y \leq 15\):
\(2(-3) - 5(-3) = -6 + 15 = 9 \leq 15\) (true).
Substitute into \(4x + y \leq -4\):
\(4(-3) + (-3) = -12 - 3 = -15 \leq -4\) (true).

Answer:

(-2, -5)