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Below are two inequalities and the graphs of their lines without the shading. By imagining

where the shading should be, identify which point would satisfy BOTH inequalities.
y <-
5
4
45
x +4
x
1

Below are two inequalities and the graphs of their lines without the shading. By imagining-example-1
User Nick Whiu
by
8.1k points

1 Answer

2 votes

Explanation:

many greetings to your teacher from me. this question is very imprecise.

a system of inequalities has very, VERY rarely only one point as solution. it normally has a whole area as solution.

as is the case here.

what we can do is find points as example representing that area.

the line of the first inequality (with -5/4 as factor of x and therefore the slope of the line) is represented by the line going from the upper left to the lower right and has a shading left/below the line (because of "<").

the line of the second inequality (with 4/5 as factor of x and therefore the slope of the line) is represented by the line going from the bottom left to the upper right and has a shading left/above the line (because of ">").

the solution area (that is all the points satisfying both inequalities) is the left pizza slice shaped quarter with its right tip being the line crossing point at about (2.4, 1).

points in that area are e.g.

(0, 0), (0, 1), (0, 2), (-1, 0), (-2, 0), (1, 1), (-2, 3), ...

the crossing point of the lines does NOT satisfy the inequalities, because both lines themselves (and therefore also the intersection point) are excluded from the inequalities (dotted lines caused by using only "<" and ">" instead of "<=" and ">=").

User ATJ
by
8.0k points