Question

1 which ordered pair is a solution to the system of inequalities shown?
a) (8, mrs. wilson
b) (2, 3) mr. browning
c) (-6, -2) mrs. lovett
d) (-4, 10) mr. tundo
e) (5, -7) ms. kress

x - 3y ≤ 18
x + 2y ≤ -2

Explanation:

Step1: Recall the system of inequalities

We have the system: \(

$$\begin{cases} x - 3y \leq 18 \\ x + 2y \leq -2 \end{cases}$$

\)

Step2: Test Option A: \((8,?)\) (Assuming the y - value is missing, but likely a typo. Let's assume A is \((8, y)\), but since we can't test properly, move to other options)

Step3: Test Option B: \((2, 3)\)

• For \(x - 3y \leq 18\): Substitute \(x = 2\), \(y = 3\). \(2-3\times3=2 - 9=-7\leq18\) (True)
• For \(x + 2y \leq -2\): Substitute \(x = 2\), \(y = 3\). \(2+2\times3=2 + 6 = 8\leq - 2\) (False). So B is not a solution.

Step4: Test Option C: \((-6, -2)\)

• For \(x - 3y \leq 18\): Substitute \(x=-6\), \(y = - 2\). \(-6-3\times(-2)=-6 + 6=0\leq18\) (True)
• For \(x + 2y \leq -2\): Substitute \(x=-6\), \(y=-2\). \(-6+2\times(-2)=-6-4=-10\leq - 2\) (True). Both inequalities are satisfied.

(We can check D and E for completeness, but since C works, we can conclude)

Step5: Test Option D: \((-4, 10)\)

• For \(x - 3y \leq 18\): Substitute \(x=-4\), \(y = 10\). \(-4-3\times10=-4 - 30=-34\leq18\) (True)
• For \(x + 2y \leq -2\): Substitute \(x=-4\), \(y = 10\). \(-4+2\times10=-4 + 20 = 16\leq - 2\) (False). So D is not a solution.

Step6: Test Option E: \((5, -7)\)

• For \(x - 3y \leq 18\): Substitute \(x = 5\), \(y=-7\). \(5-3\times(-7)=5 + 21=26\leq18\) (False). So E is not a solution.

Answer:

C. \((-6, -2)\) (Mrs. Lovett)