To find the solution to the system of inequalities, we need to find the values of x and y that make both inequalities true. To do this, we can graph the two inequalities on the same coordinate plane and find the point where the two graphs intersect.
The inequality y <= 2/3x + 1 can be graphed as a line with a slope of 2/3 and y-intercept of 1. The inequality y > -1/4x + 2 can be graphed as a line with a slope of -1/4 and y-intercept of 2.
The point of intersection between the two lines is (6,4/3). This point is included in the solution to the system, so the correct answer is (6,4/3). Note that the other ordered pairs given in the options are not included in the solution.
Answer:
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Given system of inequalities:
Plot the inequality and the given points to determine which of them fall into solution area.
See attached.
As we see only two points fall in the solution area, brown zone on the bottom: (6, −2), (6, 0.5).
