Exhibit graphically the solution set of the lineat inequations :

1.	Exhibit graphically the solution set of the lineat inequations :
Answer» Solution :(I ) First, we draw the GRAPH of`x + 2Y le 10 ` Consider the linex+ 2y 10 Clearly, the points A(0, 5) and B(l0, 0) satisfy, x + 2y = 10 Then, line AB represents x + 2y = 10. Clearly, (0, 0) satisfies the inequation ` x+ 2y le 10 ` THUS, the line AB and PART of the plane containing 0(0, 0) represent the solution set of `x + 2y le10` (ii) Next, we draw the graph of `x + y le 6`. Consider the line, x + y = 6. Clearly, the points C(O, 6) and D(6, 0) satisfy x + y = 6. So, line CD represents x + y = 6. Clearly, (0, 0) satisfies the inequation, `x + y le 6` So, the line CD and part of the plane containing 0(0, 0) represent the solution set of `x + y le 6` (iii) Next, we draw the graph of `x le 4` We know that x = 4 is the line EF parallel to the y-axis and passing through the point E(4, 0). Clearly, (0, 0) satisfies the inequation, `x le 4` Thus, the line EF and part of the plane containing 0(0, 0) represent the solution set of `x le 4` (IV)`x ge 0 ` is represented by the y-axis and the plane on its right. (v)`y ge 0 ` is represented by the x-axis and the plane above the x-axis. The intersection of all these planes is the shaded part, which together with its boundary represents the solution of the given systemof inequations.

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