# 10.6.2. Solving Systems of Linear Inequalities Graphically

State the system of inequalities whose solution is represented by the following graph.

• A, , , ,
• B, , , ,
• C, , , ,
• D, , , ,

### Example

State the system of inequalities whose solution is represented by the following graph.

### Solution

The graph is in the first quadrant only, and the - and -axes are solid, so and . Also, the boundary lines of one of the compound inequalities in the system are and . Since is solid, is dashed, and the region between them is coloured, the inequality is .

The boundary lines of the other compound inequality in the system are and . Since both lines are solid, and the region between them is coloured, the inequality is .

The boundary line of the additional inequality in the system passes through the points and . Calculate the line's slope, or , as follows:

The line's -intercept, or , is 8, so in slope-intercept form, or , the line's equation is . The line is solid, and the region below it is coloured, so the inequality is . Rewrite the inequality in standard form.

This means the system of inequalities whose solution is represented by the graph is , , , , .

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