Question

1 which ordered pair is a solution to the system of inequalities shown? x - 3y ≤ 18 x + 2y ≤ -2 a) (8, -1) mrs. wilson b) (2, 3) mr. browning c) (-6, -2) mrs. lovett d) (-4, 10) mr. tundo e) (5, -7) ms. kress

Explanation:

Step1: Test Option A (8, -1)

Substitute \(x = 8\), \(y=-1\) into \(x - 3y\leq18\):
\(8-3\times(-1)=8 + 3=11\leq18\) (true).
Substitute into \(x + 2y\leq - 2\):
\(8+2\times(-1)=8 - 2 = 6\leq - 2\) (false). So A is not a solution.

Step2: Test Option B (2, 3)

Substitute \(x = 2\), \(y = 3\) into \(x - 3y\leq18\):
\(2-3\times3=2 - 9=-7\leq18\) (true).
Substitute into \(x + 2y\leq - 2\):
\(2+2\times3=2 + 6 = 8\leq - 2\) (false). So B is not a solution.

Step3: Test Option C (-6, -2)

Substitute \(x=-6\), \(y = - 2\) into \(x - 3y\leq18\):
\(-6-3\times(-2)=-6 + 6 = 0\leq18\) (true).
Substitute into \(x + 2y\leq - 2\):
\(-6+2\times(-2)=-6 - 4=-10\leq - 2\) (true). Both inequalities hold.

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

Step4: Test Option D (-4, 10)

Substitute \(x=-4\), \(y = 10\) into \(x - 3y\leq18\):
\(-4-3\times10=-4 - 30=-34\leq18\) (true).
Substitute into \(x + 2y\leq - 2\):
\(-4+2\times10=-4 + 20 = 16\leq - 2\) (false). So D is not a solution.

Step5: Test Option E (5, -7)

Substitute \(x = 5\), \(y=-7\) into \(x - 3y\leq18\):
\(5-3\times(-7)=5 + 21=26\leq18\) (false). So E is not a solution.

Answer:

C) \((-6, -2)\)