Left some two numbers is at least negative -3 The difference of the number is less than nine

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John M. | John - Algebra TutorJohn - Algebra Tutor

The sum of 2 numbers (x and y) at least -3. (at least = greater than)

The difference between the two numbers (x and y) is less than 9.

This gives us a system of two equations, with two unknowns.

x+y=-3

x-y=9

(Note we'll deal with the inequalities in a minute)

if we solve the second equation for x, we get x=9+y.

substituting into the first equation:

9+y+y=-3, which can be solved easily for y. y=-6

Putting the value of y into the 3rd equation, x=(9+-6) = 3

So we have y=-6, and x=3. But those are NOT the answers, becuase really we are looking for the set of number for which:

x+y>-3

x-y<9

to determine whether we want values greater than or less than the found values, the easiest way is to pick a number less than or greater than those values and test them.

if we let x=2 and y=-5 then:

2-5=-3 and 2+5=7

So we know that x < 3 and y>-6.

Note that you could also have substituted the x and y equality values into the inequalities and found the same answers.

x+y≥-3

x-y<9 or y-x>-9

Rewrite as y≥-x-3

Rewrite as y>x-9

We want the area of the plane on or above the first line y=-x-3 and above the second line y=x-9.

They intersect at the point where x-9=-x-3 or 2x=6 or x=3. The point on the lines is (3,-6).

The area in question looks like a quarter of a plane with its corner at (3,-6) and opening toward the top.

The left edge is included and the right edge is missing.

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