Exhibit graphically the solution set of the lineat inequations :

Explanation

(I ) First, we draw the graph of `x + 2y le 10 `
Consider the line x+ 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 le 10`
(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 system of inequations.