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# Solve the Following System of Inequalities Graphically: X + Y ≤ 9, Y > X, X ≥ 0 - CBSE (Arts) Class 11 - Mathematics

ConceptSolution of System of Linear Inequalities in Two Variables

#### Question

Solve the following system of inequalities graphically: x + y ≤ 9, y > xx ≥ 0

#### Solution

x + y ≤ 9      ... (1)

y > x             ... (2)

x ≥ 0             ... (3)

The graph of the lines, x + y= 9 and y = x, are drawn in the figure below.

Inequality (1) represents the region below the line, x + = 9 (including the line x + y = 9).

It is observed that (0, 1) satisfies the inequality, y > x. [1 > 0]

Therefore, inequality (2) represents the half plane corresponding to the line, y = x, containing the point (0, 1) [excluding the line y = x].

Inequality (3) represents the region on the right hand side of the line, x = 0 or y-axis (including y-axis).

Hence, the solution of the given system of linear inequalities is represented by the common shaded region including the points on the lines, x + y = 9 and x = 0, and excluding the points on line y = x as follows. Is there an error in this question or solution?

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Solution Solve the Following System of Inequalities Graphically: X + Y ≤ 9, Y > X, X ≥ 0 Concept: Solution of System of Linear Inequalities in Two Variables.
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