Which of the following points are solutions to the system of inequalities shown below? y>6x + 5; color(white)("d")y<-6x + 7y>6x+5;dy<−6x+7 ?

The choices are:color(white)("d")(2, 17);color(white)("d")(-2, 19);color(white)("d")(2, 18);color(white)("d")(0, 6);color(white)("d")(8, 8);color(white)("d")(-2, 18)d(2,17);d(−2,19);d(2,18);d(0,6);d(8,8);d(−2,18)

1 Answer
Alan P.
Jun 17, 2018

Only (0,6)(0,6) and (-2,18)(−2,18) satisfy both y > 6x+5y>6x+5 and y < -6x+7y<−6x+7

Explanation:

The normal way to do this would have been by plotting the solution area, but the points can be evaluated using a simple table:

{: (ul(x),ul(y),ul(6x+5),ul(y > 6x+5),,ul(-6x+7),ul(y < -6x+7),,ul("both conditions?")), (2,17,17,color(red)("No"),,-5,color(red)("No"),,color(red)("NO")), (-2,19,-7,color(blue)("Yes"),,19,color(red)("No"),,color(red)("NO")), (2,18,17,color(red)("No"),,-5,color(red)("No"),,color(red)("NO")), (0,6,5,color(blue)("Yes"),,7,color(blue)("Yes"),,color(blue)("YES")), (8,8,53,color(red)("No"),,-41,color(red)("No"),,color(red)("NO")), (-2,18,-7,color(blue)("Yes"),,19,color(blue)("Yes"),,color(blue)("YES")) :}

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