#### Question

Solve the following system of inequalities graphically: 4*x* + 3*y* ≤ 60, *y* ≥ 2*x*, *x* ≥ 3, *x*, *y* ≥ 0

#### Solution

4*x* + 3*y* ≤ 60 … (1)

*y* ≥ 2*x* … (2)

*x* ≥ 3 … (3)

The graph of the lines, 4*x* + 3*y* = 60, *y* = 2*x*, and *x* = 3, are drawn in the figure below.

Inequality (1) represents the region below the line, 4*x* + 3*y* = 60 (including the line 4*x* + 3*y* = 60). Inequality (2) represents the region above the line, *y* = 2*x *(including the line *y* = 2*x*). Inequality (3) represents the region on the right hand side of the line, *x* = 3 (including the line *x* = 3).

Hence, the solution of the given system of linear inequalities is represented by the common shaded region including the points on the respective lines as follows.

Is there an error in this question or solution?

Solution Solve the Following System of Inequalities Graphically: 4x + 3y ≤ 60, Y ≥ 2x, X ≥ 3, X, Y ≥ 0 Concept: Solution of System of Linear Inequalities in Two Variables.