Question

Graph the system of inequalities to show all possible solutions.
{y<3x-2
{y ≥ -x+3

Answer 1

Explanation:

The solution is a darkest area of a plane. All dots inside this area are the solutions of the system.

Answer 2

see attachment for graph

Explanation:

< or > : dashed line

≤ or ≥ : solid line

< or ≤ : shade below the line

> or ≥ : shade above the line

To graph the line y < 3x-2

Rewrite the equation as: y = 3x - 2

Find two points on the line:

when x = 0, y = 3(0) - 2 = -2 → (0, -2)

when x = 3, y = 3(3) - 2 = 7 → (3, 7)

Plots the found points (0, -2) and (3, 7).

Draw a straight, dashed line through the points.

To graph the line y ≥ -x + 3

Rewrite the equation as: y = -x + 3

Find two points on the line:

when x = 0, y = -(0) + 3 = 3 → (0, 3)

when x = 3, y = -(3) + 3 = 0 → (3, 0)

Plots the found points (0, 3) and (3, 0).

Draw a straight, solid line through the points.

Shade above the solid line and below the dashed line to the right of where the two lines intersect. The shaded area is the area of all possible solutions.