Question

A set of points in the xy-coordinate plane meets two conditions, as described.

Condition 1: the y-coordinate is positive
Condition 2: the sum of the coordinates is more than -2
Create a system of inequalities described by the two conditions.

Answer 1

Condition 1: y>0

Condition 2: x+y>-2

Explanation:

We are told that we have a set of points in the Cartesian system (i.e. x-y coordinate), so we can define our point as:

`(x,y)`

We are given two conditions and we want to create a system of inequalities. Now, generally speaking, inequalities are expressions relating mathematical expressions through 'comparison' (i.e. less than, greater than, or less/greater and equal to) usually recognized by
`<`,
`>`,
`\leq` and
`\geq`, respectively.

So in our case let set up our inequalities.

Condition 1: the y-coordinate is positive

This can be mathematically translated as

`y>0`

(i.e.
`y` is greater than 0, therefore positive)

Condition 2: the sum of the coordinates is more than -2

This can be mathematically translated as

`x+y>-2`

(i.e. the summation of the two coordinates is greater than -2 but not equal to).

The system of inequalities described by the two conditions is:

`y>0\\x+y>-2`