# 10.6.2. Solving Systems of Linear Inequalities Graphically

A shepherd wants to build a rectangular sheep barn, and the graph represents the relation between the dimensions of the needed barn, where x represents the width and y represents the length. State the system of inequalities that describes the dimensions of the barn.

• A, , ,
• B, , ,
• C, , ,
• D, , ,

### Example

A shepherd wants to build a rectangular sheep barn, and the graph represents the relation between the dimensions of the needed barn, where x represents the width and y represents the length. State the system of inequalities that describes the dimensions of the barn.

• A, , ,
• B, , ,
• C, , ,
• D, , ,

### Solution

The graph is in the first quadrant only, and the - and -axes are solid, so and . Also, the boundary line of one of the inequalities in the system is . The line is solid, and the region above it is coloured, so the inequality is . The boundary line of the other inequality in the system passes through the points and . Calculate the line's slope, or , as follows.

The line's -intercept, or , is 88.5, 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 . Transform the inequality.

This means the system of inequalities that describes the dimensions of the barn is , , , .

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