SOLUTION: Determine whether each ordered pair is a solution to the inequality −5x+2y<0 8,−10) (0,−5) (−1,−6) (−4,−2) (−7,4)

Question 1182457: Determine whether each ordered pair is a solution to the inequality −5x+2y<0
8,−10)
(0,−5)
(−1,−6)
(−4,−2)
(−7,4)
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Determine whether each ordered pair is a solution to the inequality
(,)

->true=> (,) is a solution to the inequality

(,)

->true=> (,) is a solution to the inequality

(,)

->true=> (,) is a solution to the inequality

(,)

->false=> (,) is a solution to the inequality

(,)

->false=> (,) is a solution to the inequality

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Check out this similar problem
https://www.algebra.com/algebra/homework/expressions/expressions.faq.question.1182456.html

Hopefully that's enough to tackle this current problem. If not, then I'll show you how to solve.

Let's draw the graph.

The boundary line is the equation -5x+2y = 0, which is the same as y = (5/2)x. This line goes through (0,0) and (2,5). We make the boundary line a dashed line to tell the reader "points on the boundary are not solutions".

If we plugged in the coordinates of choice A(8,-10), then we get
-5x+2y < 0
-5(8)+2(-10) < 0
-40-20 < 0
-60 < 0
This is a true statement since -60 is smaller than 0. On a number line, -60 is to the left of 0. The last inequality being true indicates the first one is true when (x,y) = (8,-10)

Because -5x+2y < 0 is true for choice A, this means we shade the entire region in which point A is located. This shades below the dashed boundary line as shown below

Graph of -5x+2y < 0

Points A, B, C are in the shaded region. Therefore, they are solution points. In contrast, points D and E are not solutions as they are outside the shaded region.

A non-visual approach is to plug the coordinates of each point into the inequality to see which result in true statements or not. You should find that points A through C result in true statements while D and E lead to false statements.

Here's an example of a false statement
We'll plug in the coordinates for choice D
-5x+2y < 0
-5(-4)+2(-2) < 0
20-4 < 0
16 < 0
we can see this is false because it should be 16 > 0

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