In Exercises 1–4, solve the systems of equations.
1.
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College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)
- Exercises 38–40 will help you prepare for the material covered in the first section of the next chapter. In Exercises 38-39, simplify each algebraic expression. 38. (-9x³ + 7x? - 5x + 3) + (13x + 2r? – &x – 6) 39. (7x3 – 8x? + 9x – 6) – (2x – 6x? – 3x + 9) 40. The figures show the graphs of two functions. y y 201 10- .... -20- flx) = x³ glx) = -0.3x + 4x + 2arrow_forwardIn Exercises 15–16, solve each system by eliminating variables using the addition method. 15. [3x + 12y = 25 |2r - 6y = 12 x + 3y -x + 2y + 3z 2х - 5у — г 16. 5 13 -8arrow_forwardFor Exercises 41–54, write the equation in the form (x – h + (y – k)' = c. Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4) 41. x + y? - + 6x – 2y + 6 = 0 42. x + y + 12x – 14y + 84 = 0 43. x + y 22x + 6y + 129 = 0 44. x + y? - 10x + 4y – 20 = 0 45. x + y - 20y – 4 = 0 46. x + y + 22x – 4 = 0 47. 10x + 10y² – 80x + 200y + 920 = 0 (Hint: Divide by 10 to make the x and y2 term coefficients equal to 1.) 48. 2x + 2y? 32x + 12y + 90 = 0 49. x + y? – 4x – 18y + 89 = 0 50. x + y - 10x – 22y + 155 = 0 51. 4x? + 4y 20y + 25 = 0 52. 4x + 4y? 12x + 9 = 0 53. x + y - x - 3 3 -y - 54. x + v? 2 = 0 = 0 9. -X - 2 4 3 3arrow_forward
- In Exercises 9–12, find all real solutions to the equations.arrow_forwardExercises 99–108: Solve the given equation for the specified variable. 101. P = 2L + 2W for Larrow_forwardIn Exercises 23–25, solve each equation. If the solution set is Ø or (-0, ), classify the equation as an inconsistent equation or an identity. 23. 3(2x – 4) = 9 – 3(x + 1) 2x 24. x - 4 x + 1 4 2 4 25. 3(x – 4) + x = 2(6 + 2x)arrow_forward
- In Exercises 3–6, solve each system by graphing. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 3. x + y = 5 3x - y = 3 4. [3x – 2y = 6 16x – 4y = 12 3 y 6. [y = -x + 4 |3x + 3y = -6 5. 5h 2х — у %3D — 4arrow_forwardFor Exercises 73–80, (a) evaluate the discriminant and (b) determine the number and type of solutions to each equation. (See Example 9) 73. Зх? 4х + 6 3D 0 74. 5x - 2x + 4 = 0 75. - 2w? + 8w = 3 76. -6d + 9d = 2 77. Зx(х — 4) 3D х — 4 78. 2x(x – 2) = x + 3 79. –1.4m + 0.1 = -4.9m² 80. 3.6n + 0.4 = -8.1n?arrow_forwardIn Exercises 43–54, solve each absolute value equation or indicate the equation has no solution. 43. |x – 2| = 7 45. |2x – 1| = 5 47. 2|3x – 2| = 14 44. |x + 1| = 5 46. |2r – 3| = 11 48. 3|2x – 1| = 21 %3D %3D 5 24 - + 6 = 18 50. 4 1 x + 7 = 10 51. |x + 1| + 5 = 3 53. |2x – 1| + 3 = 3 52. |x + 1| + 6 = 2 54. |3x – 2| + 4 = 4arrow_forward
- For Exercises 15–22, solve the system by using the addition method. (See Examples 3-4) 15. 2x + 3y = 11 16. 3x + y² = 21 17. x - xy = 20 18. 4xy + 3y² = -9 2 + 4y = 8 4x - 2y = -2 -2x2 + 3xy = -44 2xy + y = -5 21. x = 1- y 9x - 4y? = 36 19. 5x - 2y2 = 1 20. 6x + 5y = 38 7x - 3y = 9 22. 4x = 4 - y? 16y = 144 + 9x? 2x - 3y = -4arrow_forwardIn Exercises 31–32, solve each formula for the specified variable. 1 31. V = - lwh for h 3 32. Ax + By = C for yarrow_forwardIn Exercises 49–54, solve for y in terms of t or x, as appropriate.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt