Question

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A student proposed the following method of sketching the solution to a system of two inequalities. “First, I shade the region of points that satisfies the first inequality. Then, I shade the region of points that satisfy the second inequality. The solution consists of all points that have been shaded.” Do you agree? Explain. Support your answer using the system 5x-3y>1
and 3x+4y<=18

Answer 1

The solution to a system of inequalities is the "intersection" of each different inequality's solution.
a. 5x-3y>1 becomes y>(1-5x)/3. the line intersects the x-axis in 1/5 and it is negative sloped (-5/3). Draw the line on a x-y graph and shape its right side with blue.
b. 3x+4y<=18 becomes y<=(18-3x)/4. the line intestects the x-axis in 18/3 and it is negative sloped (-3/4), but flatter than a. draw the line and shape its left side with red.
the only part of the graph shaped with both blue and red is the solution of the system!

Answer 2

Thank you so much!!