Is #(-3,2)# a solution of #-4x-10y<-9#?

1 Answer
Geoff K.
Dec 10, 2016

No, #("-"3,2)# is not a solution of #"-"4x-10y<"-"9.#

Explanation:

An inequality like this one represents an area of points on the #x"-"y# plane with a line-shaped boundary on one "side". Solutions to this inequality are all points #(x,y)# such that #"-"4x-10y<"-"9.#

To test if a point is part of the solution set, we simply plug that point's coordinates into the inequality, and see if it simplifies to a true statement. In other words, the statement

"#("-"3,2)# is a solution to #"-"4x-10y<"-"9#"

is identical to

#"-"4("-"3)-10(2)<"-"9#

which simplifies to

#12-20<"-9"#
#"-"8<"-"9#

But this is not a true statement. Thus, the point #(x,y)=("-"3,2)# is not a solution of #"-"4x-10y<"-"9.#

Here's a graph of the inequality; the point #("-"3,2)# lies just below the boundary line:
graph{-4x-10y<-9 [-6, 4, -2, 3]}

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