solve inequalities by graphing

Question

2x + y >= 4

y <= -2x - 1

Answer 1

Given inequalities are 2x+y ≥ 4

y ≤ -2x-1

Draw the coordinate plane.

Graph the lines y = -2x+4 and y = -2x-1.

The graph of y = -2x+4 is solid and is included n the graph of the solution and the graph of y = -2x-1 is

solid and included the graph of the solution.

The graph of 2x+y ≥ 4 is shaded with aqua colour and graph of y ≤ -2x-1 is shaded with olive colour.

The boundary of the inequlity 2x+y ≥ 4 is shaded with merun colour and the boundary of the inequality

y ≤ -2x-1 is shaded with blue colour.

The graph of y = -2x-1 and y = -2x+4 are parallel lines.The two regions do not intersect at any point,

so the system has no solution.