7. Systems of Equations & Matrices

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x²+y²≤16, x+y>2

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In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x²+y²>1, x²+y²<16

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In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. (x−1)²+(y+1)²<25, (x−1)²+(y+1)²≥16

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x²+y²≤1, y−x²>0

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In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x²+y²<16, y≥2^x

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. 3x+y≤6, 2x−y≤−1, x>−2, y<4

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x≥0, y≥0, 2x+ 5y< 10, 3x + 4y ≤ 12

In Exercises 63–64, write each sentence as an inequality in two variables. Then graph the inequality. The y-variable is at least 4 more than the product of -2 and the x-variable.

In Exercises 65–68, write the given sentences as a system of inequalities in two variables. Then graph the system. The sum of the x-variable and the y-variable is at most 4. The y-variable added to the product of 3 and the x-variable does not exceed 6.

In Exercises 65–68, write the given sentences as a system of inequalities in two variables. Then graph the system. The sum of the x-variable and the y-variable is no more than 2. The y-variabe is no less than the difference between the square of the x-variable and 4.

In Exercises 69–70, rewrite each inequality in the system without absolute value bars. Then graph the rewritten system in rectangular coordinates. |x|≤2, |y|≤3

In Exercises 57–59, graph the region determined by the constraints. Then find the maximum value of the given objective function, subject to the constraints. This is a piecewise function. Refer to the textbook.

In Exercises 57–59, graph the region determined by the constraints. Then find the maximum value of the given objective function, subject to the constraints. This is a piecewise function. Refer to the textbook.

Find the value of the objective function z = 2x + 3y at each corner of the graphed region shown. What is the maximum value of the objective function? What is the minimum value of the objective function?