Question

Solve the inequalities $x+y\le 9,y>x$ and $x\ge 1$ graphically.

Answer 1

We have,

$x+y\le 9$

y > x and $x\ge 1$

Converting the inequalities into equations, we obtain

x + y = 9, y = x and x = 1

Region represented by $x+y\le 9$

Its equation form is x + y = 9

$\begin{array}{ccc}x& 0& 9\\ y& 9& 0\end{array}$

The line x + y = 9 meets the coordinate axes at A(9, 0) and B(0, 9) respectively. Join these points by a dark line. Clearly, (0, 0) satisfies the inequality $x+y\le 9.$ So, half plane of $x+y\le 9$ contains the origin.

Region represented by y > x

Its equation form is y = x

$\begin{array}{cccc}x& 0& 1& 2\\ y& 0& 1& 2\end{array}$

The line y = x passes through the point (0, 0), (1, 1) and (2, 2), respectively. Join these points by a dark line. Clearly, (1, 0) does not satisfy the inequality y > x So, half plane of y > x does not contain (1, 0).

Region represented by x = 1

Its equation form x = 1

$\begin{array}{ccc}x& 1& 1\\ y& 0& 2\end{array}$

The equation of line x = 1 plane, through (1, 0) and (1, 2), Clearly, (0, 0) does not satisfy the inequalities $x\ge 1.$ So, half plane does not contain the origin.