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Name_______________________________ Algebra 1 Unit 6 Review 1. Is (-2, 3) a solution to the following system? y = -x + 1 y = ½x + 4 2. Is (4, -1) a solution to the following system? 3x + y > 8 x – 2y < 4 For problems 3 - 6 state determine how many solutions the system has. 3. y = 3x + 1 y = 3x + 1 4. y = ⅓x + 6 y = ⅓x – 2 5. y = ½x – 4 y = ¼x + 9 6. 10x – 4y = 12 5x – 2y = 6 7. 3x – 7y = 10 -9x + 21y = 15 8. Multiple choice: At what point do the lines defined by the equations x + y = 15 and x – y = -1 intersect? 12 1 A (10, 5) B , C (-1, 15) D (7, 8) 5 5 In 9 – 10, solve the systems of equations by graphing. 9. y = x + 1 2 y= x+4 5 10. y = -2x - 6 y 3 x5 4 In 11 - 13, solve the systems of equations by the substitution method. 11. x = y – 3 4x + 2y = 48 12. 3x – 4y = -11 y = 2x - 1 13. y = 4x – 13 y = -x – 3 In 14 - 16, solve the systems of equations by the addition/elimination method. 14. 2x + 4y = -14 3x – 4y = 9 15. 3x – 2y = 6 6x + 5y = 12 16. 4x + 3y = 23 7x – 2y = 4 17. Graph: 2x – 4y < 12 Graph the solution set to the following sets of inequalities. 18. x > 2 19. 2 y< x–4 3 y > –2x y < ⅓x – 2 Chapter 2, 3, and 5 Review Solve the following equations. 20. 2 x + 2 = 20 3 21. 2(3x + 4) – 3 = -13 22. 5 2 x4 x6 23. x 3 2 3 5 3 24. 3x x 5 4 2 25. 2x 1 7 26. x 8 5 9 For problems 27 – 29, state whether the equation has one solution, no solutions, or if it is an Identity (Infinitely Many Solutions) 27. 4(x – 3) = 4x – 12 28. 10x – 3x – 9 =4 30. Find the x-intercept and the and y-intercept: 29. 2x + 6(x + 1) = 4(2x – 3) 2x + 3y = 12 31. Find the slope and y-intercept: x – 4y = 8 32. Write the equation for the line containing the point (6, -1) that has slope of 1 . 2 33. Find the equation of the line that passes through the points (2, 7) and (-4, -5). 34. Find the equation of the line that passes through the point (-2, -7) that is parallel to the line y = 3x + 1. 35. Are the two lines 3x – y = -7 and x + 3y = 6 parallel or perpendicular?