7. Systems of Equations and Inequalities

Match each system of inequalities with the correct graph from choices A–D. x ≥ 5 y ≤ -3

In Exercises 1–26, graph each inequality. y≤(1/3)x

In Exercises 1–26, graph each inequality. y>2x−1

Graph each inequality. x + 2y ≤ 6

In Exercises 1–26, graph each inequality. x^2+y^2≤1

Graph each inequality. 4y - 3x ≤ 5

In Exercises 1–26, graph each inequality. x^2+y^2>25

Graph each inequality. x < 3 + 2y

In Exercises 1–26, graph each inequality. y≥x^2−9

Graph each inequality. y > (x - 1)^2 + 2

In Exercises 1–26, graph each inequality. y>2^x

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. 2x−5y≤10, 3x−2y>6

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

Work each problem. Write the inequality that represents the region inside a circle with center (-5, -2) and radius 4.

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. −2≤x<5

In Exercises 39–45, graph each inequality. 3x - 4y > 12

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x−y≤1, x≥2

In Exercises 39–45, graph each inequality. y ≤ (-1/2)x + 2

Graph the solution set of each system of inequalities. 3x + 5y ≤ 15 x^2 + y^2 < 9

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. y≥x^2−1, x−y≥−1

In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.

This

is a piecewise function. Refer to the textbook.

In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.

This

is a piecewise function. Refer to the textbook.

Graph the solution set of each system of inequalities. y ≥ x^2 + 4x + 4 y < -x^2

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x^2+y^2≤1, y−x^2>0

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 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 1–26, graph each inequality. x−2y>10

In Exercises 1–26, graph each inequality. y>−3

Graph each inequality. y < 3x^2 + 2

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. 3x+6y≤6, 2x+y≤8

Graph each inequality. y ≤ log(x - 1) - 2

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x≤2, y≥−1

Graph the solution set of each system of inequalities. 2x + y > 2 x - 3y < 6

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

In Exercises 39–45, graph each inequality. y ≤ 2^x

In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.

This

is a piecewise function. Refer to the textbook.

Graph the solution set of each system of inequalities. y ≥ (x - 2)^2 + 3 y ≤ -(x - 1)^2 + 6

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. x≥0, y≥0, 2x+ 5y< 10, 3x + 4y ≤ 12

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 1–26, graph each inequality. x+2y≤8

In Exercises 1–26, graph each inequality. x≤−3

In Exercises 1–26, graph each inequality. y>−3

In Exercises 1–26, graph each inequality. (x−2)^2+(y+1)^2<9

Graph each inequality. x ≤ 3

In Exercises 1–26, graph each inequality. y≥log_2(x+1)

Graph each inequality. y > 2^x + 1

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. 3x+6y≤6, 2x+y≤8

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

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x≤2, y≥−1

Graph the solution set of each system of inequalities. x + y ≥ 0 2x - y ≥ 3

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

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

In Exercises 39–45, graph each inequality. y ≤ x^2 - 1

Graph the solution set of each system of inequalities. x + 2y ≤ 4 y ≥ x^2 - 1

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x^2+y^2>1, x^2+y^2<16

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

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 1–26, graph each inequality. y>2x−1

In Exercises 1–26, graph each inequality. x≤−3

In Exercises 1–26, graph each inequality. (x−2)^2+(y+1)^2<9

Graph each inequality. 2x > 3 - 4y

Graph each inequality. x^2 + (y + 3)^2 ≤ 16

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

Match each inequality with the appropriate calculator graph in A–D. Do not use a calculator y ≤ -3x - 6

In Exercises 39–45, graph each inequality. y ≤ (-1/2)x + 2

Graph the solution set of each system of inequalities. 4x - 3y ≤ 12 y ≤ x^2

In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.

This

is a piecewise function. Refer to the textbook.

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

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

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.