Question

42 POINTS!!! +BRAINLIEST




Given the system y > -2 x + y < 4


1. Name an ordered pair that IS a solution to this system and explain how you know that this is a solution point.

2. Name an ordered pair that is not a solution to the system and explain how you know that it is not a solution.

Tip: You may want to look at the graph of the system. Desmos is a tool that you can use to help you visualize the graph.

Answer 1

Given system of equation is:

y>-2

x+y<4

First we need to graph both on same paper then we can easily find the required points.

Graphing y>-2

there is no x in this inequality so the graph will be a horizontal line passing through -2 on y-axis.

Shading will be upward because of > sign as shown in picture.

Graphing x+y<4

plug any number for x or y to get other value

Let's plug x=0

0+y<4

y<4

so the first point is (0,4)

similarly by plugging y=0, we get (4,0)

now draw a dotted line joining both points

shading will be towards origin because origin (0,0) satisfies x+y<4

So the final graph will look like :

Ans(1):

We can choose any point (orderd pair) which lies in common shaded region so that can be (0,0).

To double check you can also plug (0,0) into given inequalities to see if they satisfy this point or not.

Ans(2):

We can choose any point (orderd pair) which DOESN'T lies in common shaded region so that can be (5,5).

To double check you can also plug (5,5) into given inequalities to see if they satisfy this point or not.