In Exercises 27-62, graph the solution set of each system of inequalities or indicate that the system has no solution.
45.
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- In Exercises 65-68, write the given sentences as a system of inequalities in two variables. Then graph the system. 65. 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. 66. The sum of the x-variable and the y-variable is at most 3. The y-variable added to the product of 4 and the x-variable does not exceed 6. 67. The sum of the x-variable and the y-variable is no more than 2. The y-variable is no less than the difference between the square of the x-variable and 4. 68. The sum of the squares of the x-variable and the y-variable is no more than 25. The sum of twice the y-variable and the x-variable is no less than 5.arrow_forwardThe graphs of solution sets of systems of inequalities involve finding the intersection of the solution sets of two or more inequalities. By contrast, in Exercises 53–54 you will be graphing the union of the solution sets of two inequalities. 53. Graph the union of y >x – 2 and y < 4. 54. Graph the union of x – y 2 -1 and 5x – 2y < 10.arrow_forwardIn Exercises 47–48, write each sentence as a linear inequality in two variables. Then graph the inequality. 47. The y-variable is at least 4 more than the product of -2 and the x-variable. 48. The y-variable is at least 2 more than the product of -3 and the x-variable.arrow_forward
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- Find the y-intercept and x-intercept of the linear inequalities then graph the system. 1.2х + 3у > 6; 2.4x + y > 2; x-y33 3.2х — Зу > -9; 4x + 3y < -9arrow_forwardDetermine whether each ordered pair is a solution of the inequality x+y>5. (1,4), (4,6), (−2,8) Is the ordered pair (1,4) a solution of the linear inequality? Yes No Is the ordered pair (4,6) a solution of the linear inequality? No Yes Is the ordered pair (−2,8) a solution of the linear inequality? Yes Noarrow_forwardIn Exercises 1–5, solve each equation, inequality, or system. 1. 2x + 5 s 11 and -3x > 18 2. 2x2 = 7x + 4 4х + Зу + 3z + 2z 2x – 5y 3. 4 3x 2 = -4 4. |3x – 4| < 10 6. 5. X - 8 x2 - 10x + 16 -xarrow_forward
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