Question

multiple choice

1. the point which is not in the solution region of the inequality (4x - 3y leq 6) is

a. ((0,0))
b. ((-1,2))
c. ((1,-2))
d. ((3,2))

Explanation:

Step1: Substitute option A \((0,0)\)

Substitute \(x = 0,y = 0\) into \(4x-3y\leq6\):
\(4(0)-3(0)=0\leq6\), which is true. So \((0,0)\) is in the solution region.

Step2: Substitute option B \((-1,2)\)

Substitute \(x=-1,y = 2\) into \(4x-3y\):
\(4(-1)-3(2)=-4 - 6=-10\leq6\), which is true. So \((-1,2)\) is in the solution region.

Step3: Substitute option C \((1,-2)\)

Substitute \(x = 1,y=-2\) into \(4x-3y\):
\(4(1)-3(-2)=4 + 6 = 10\). Now check \(10\leq6\)? No, \(10>6\). So \((1,-2)\) is not in the solution region.

Step4: Substitute option D \((3,2)\)

Substitute \(x = 3,y = 2\) into \(4x-3y\):
\(4(3)-3(2)=12 - 6 = 6\leq6\), which is true. So \((3,2)\) is in the solution region.

Answer:

C. \((1,-2)\)