Question

$-9x + 5y \leq -6$
$4x - 8y < -16$
is $(0, 2)$ a solution of the system?
choose 1 answer:
a yes
b no

Explanation:

Step1: Substitute (0,2) into first inequality

Substitute $x=0$, $y=2$ into $-9x + 5y \leq -6$:

$$\begin{align*} -9(0) + 5(2) &= 0 + 10 = 10 \end{align*}$$

Check if $10 \leq -6$: This is false.

Step2: Substitute (0,2) into second inequality

Substitute $x=0$, $y=2$ into $4x - 8y < -16$:

$$\begin{align*} 4(0) - 8(2) &= 0 - 16 = -16 \end{align*}$$

Check if $-16 < -16$: This is false.

Step3: Evaluate system solution status

A point must satisfy all inequalities in the system to be a solution. Since (0,2) satisfies neither inequality, it is not a solution.

Answer:

B. No