QUESTION 7 The sum of two numbers, $$ x $$ and $$ y $$, is more than 6 . When you triple $$ x $$ and add it to double $$ y $$, the sum is less than 18 . Choose the graph that models this situation.

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We are given two conditions: 1. x + y > 6 2. 3x + 2y < 18 Step 1: Rewrite the equations as boundary lines. • For x + y > 6, the boundary line is x + y = 6. Its intercepts are (0, 6) and (6, 0). Because the inequality is “>”, the line is dashed. • For 3x + 2y < 18, the boundary line is 3x + 2y = 18. Its intercepts are (0, 9) and (6, 0). Since the inequality is “<”, this line is also dashed. Step 2: Determine which side of each line to shade: • For x + y > 6, if you test a point such as (0, 0), you get 0 + 0 = 0 which is not > 6, so the region satisfying x + y > 6 is the opposite half (the area above and to the right of the line). • For 3x + 2y < 18, testing (0, 0) gives 3(0) + 2(0) = 0 which is less than 18, so the region satisfying 3x + 2y < 18 is the side that includes (0, 0), i.e. below and to the left of the line. Step 3: The overall solution is the intersection of these regions. So the correct graph: • Has dashed lines for both x + y = 6 (shading above it) and 3x + 2y = 18 (shading below it). • The overlapping area (the intersection) is the solution region. Now, choose the graph that shows both dashed boundary lines with the region above the line x + y = 6 and below the line 3x + 2y = 18. The correct graph has dashed lines for $$ x + y = 6 $$ and $$ 3x + 2y = 18 $$, with the region above the first line and below the second line shaded.

QUESTION 7 The sum of two numbers, \( x \) and \( y \), is more than 6 . When you triple \( x \) and add it to double \( y \), the sum is less than 18 . Choose the graph that models this situation.

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