Question
Which point is a solution to the simultaneous inequalities y < 1/2x and y > 1/3x+3?
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GPT 3.5
To find the solution to the simultaneous inequalities y < 1/2x and y > 1/3x+3, we need to find the region where both inequalities are satisfied.
First, let's graph the equation y = 1/2x. This is a line with a slope of 1/2 and y-intercept of 0 (since there is no constant term).
Next, let's graph the equation y = 1/3x + 3. This is a line with a slope of 1/3 and y-intercept of 3.
Since y < 1/2x, the region below the line y = 1/2x is shaded.
Since y > 1/3x + 3, the region above the line y = 1/3x + 3 is shaded.
Looking at the graph, we can see that the region shaded both below the line y = 1/2x and above the line y = 1/3x + 3 is the solution to the simultaneous inequalities.
Therefore, any point in that region would be a solution.
First, let's graph the equation y = 1/2x. This is a line with a slope of 1/2 and y-intercept of 0 (since there is no constant term).
Next, let's graph the equation y = 1/3x + 3. This is a line with a slope of 1/3 and y-intercept of 3.
Since y < 1/2x, the region below the line y = 1/2x is shaded.
Since y > 1/3x + 3, the region above the line y = 1/3x + 3 is shaded.
Looking at the graph, we can see that the region shaded both below the line y = 1/2x and above the line y = 1/3x + 3 is the solution to the simultaneous inequalities.
Therefore, any point in that region would be a solution.
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