Question

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

Answer 1

Only `(0,6)` and `(-2,18)` satisfy both `y > 6x+5` and `y < -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")) :}#