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Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y > 2x + 3 y is less than negative 3 over 2 times x minus 4 Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points) Part B: Is the point (−4, 6) included in the solution area for the system? Justify your answer mathematically. (4 points)
y > 2x + 3|dw:1438795610928:dw| thats the graph
for the second part PART A the graph is |dw:1438795686827:dw|
for example A linear inequality in the two variables x and y looks like ax + by < c ax + by < c ax + by > c ax + by > c where a, b, and c are constants. A solution to an inequality is any pair of numbers x and y that satisfy the inequality. The rules for finding the solution set of a linear inequality are much the same as those for finding the solution to a linear equation. Add or subtract the same expression to both sides. Multiply or divide both sides by the same nonzero quantity; if that quantity is negative, then the inequality must be reversed. Example 1. Determine the solution set of 5x + 2y < 17. One solution to this is x = 2 and y = 3, because 5(2) + 2(3) = 16, which is indeed less than or equal to 17. A pair of numbers that does not form a solution is x = 3 and y = 2, because 5(3) + 2(2) = 19, which is not less than or equal to 17. The pair x = 2 and y = 3 isn't the only solution; as a matter of fact, there are infinitely many solutions. Since we can't write down all possible solutions to a linear inequality, a good way to describe the set of solutions to any linear inequality is by a graph. If the pair of numbers x and y is a solution, then think of this pair as a point in the plane, so the set of all solutions can be thought of as a region in the xy-plane. To illustrate how to determine this region; first, we solve the inequality for y in terms of x. 5x + 2y < 17 2y < ~5x+ 17 y < -(5/2) x + 17/2 Next, graph the line y = -(5/2) x + 17/2. The set of points (x,y) that lie on this line is the set of all (x,y) such that y is exactly equal to -(5/2) x + 17/2. These points make up part of the set of solutions to the inequality, but not all. We see that y can also be less than -(5/2) x + 17/2, so all points below the line would also be solutions. The shaded region in Figure 1 shows the solution set.
y > 2x + 3 y is less than negative 3 over 2 times x minus 4 do u know how to write it