Question

A system of linear inequalities is shown below.

x - y > 3
y + x ≤ 2

Describe the steps to graph the solution set to the system of inequalities.

Answer 1

x - y > 3

put this in y = mx + b form
-y > -x + 3
y < x - 3

slope = 1
y intercept is (0,-3)
x intercept can be found by subbing in 0 for y
x - y > 3
x - 0 > 3
x > 3
x intercept is (3,0)

since the line does not have an equal sign, you will use a dashed line
start at (0,-3) and since the slope is 1, go up one space, and to the right 1 space, then up 1 space, and to the right 1 space, keep doing this and you will cross the x axis at (3,0).

and since the ine is less then, shading occurs below the line.

y + x <= 2
y < = -x + 2

slope is 2
y intercept is (0,2)
x intercept :
y + x <= 2
0 + x <= 2
x <= 2
x intercept is (2,0)

since there is an equal sign, the line will be solid
start at (0,2) and since the slope is -1, go down 1, and to the right 1, then down 1, and to the right 1, and you will eventually cross the x axis at (2,0)

and since the inequality sign is less then, shade below the line

solution will be in the shaded regions that both lines share

Answer 2

one method
for each line set as an equation find y when x = 0 and x when y = 0 this will give 2 points connect to get the line with the eqn in the form y =mx + b replace with the inequality and shade that section the overlap with the shaded sections