Question
Match the system to the graph.
- y ≤ 3x and y ≤ -2x + 4
- y > 3x and y > -2x + 4
- y < 3x and y > -2x + 3
- y > 3x and y < -2x + 4
Hint:
First, we need to identify the equations. Then, we determine the inequalities by observing the direction of the solution region for the equations. But in the beginning, observe that both the straight lines are dotted so, both the equations should have strict inequalities without equity.
The correct answer is: y > 3x and y < -2x + 4
Step 1 of 2:
Observe that, the red dotted line attains the points: (-1,-3), (1,3), and (2,6).
Note that all the y values are multiples of 3 of the x values. So, the graph equation should be y = 3x.
Now, the red region indicates the upper side of the line, viz., higher y values.
Hence, the inequality should be y > 3x.
Step 2 of 2:
Similarly, observe that the blue dotted line attains the points: (-1,6), (1,2), and (1,2).
This matches with the graph equation y = -2x + 4
Again, the blue region indicates the lower side of the line, viz., lower y values.
Hence, the inequality should be y < -2x + 4.
Final Answer:
The graph represents system-- d. y > 3x and y < -2x + 4
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