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 49-50, write the given sentences as a system of linear inequalities in two variables. Then graph the system. 49. 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. 50. 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.arrow_forwardIn 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_forwardIn Exercises 7-10, graph each equation or inequality in a rectangular coordinate system. 7. f(x) = 2x + 1 9. 2x – y 2 6 8. y > 2x 10. f(x) = -1arrow_forward
- In Exercises 11-13, graph each equation or inequality in a rectangular coordinate system. 1 11. f(x) + 1 3 12. 4x – 5y < 20 13. y < -1arrow_forwardIn Exercises 35–40, graph each inequality in a rectangular coordinate system. 35. Зх — 4у > 12 36. х 3y =x 39. x -3arrow_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_forward
- 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_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_forwardDescribe the regions defined by the inequalities and pairs of inequalities in Exercises 31–32. 31. x2 + y2> 1, x2 + y2 < 4 32. x2 + y2 + 6y <0, y>-3arrow_forward
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