Question

How do you graph the system `y > x - 3` and `y > x`?

Answer 1

Graph and solve the system of linear equations in 2 variables:
(1) y > x - 3
(2) y > x

Explanation:

First graph the line y1 = x - 3.
The solution set of the inequality (1) (y > x - 3) is the area above this line. (Note the > sign). Shade or color this area
Next, graph the line y = x. The solution set of the inequality (2) y > x is the area above this line. Shade or color it.
The combined solution set of the system is the commonly shared area.
When do you apply the Test Point Method?
When the linear functions are expressed in standard form.
Examples:
`2x + 3y - 4 < 0; or -3x - 4y + 5 > 0; or 2x/3 - 3y/3 - 1/2 >= 0`
In these cases, you graph the 2 lines by x and y intercepts. Then, you use the test point method to determine the 2 areas of the 2 solution sets. The origin O is usually the best test point.