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99 Algebra 1 Review for Chapter 7 (And 6.7) Solving by Graphing: Graph each equation and find the point of intersection. That is the solution to the system. 1. y = 2 x 1 3 y = -x + 4 2. y = -2 2x - 5y = 10 Solving by Substitution: Isolate one variable and plug that into the other equation. Then solve for the variable that is left. Then plug that value into either original equation and solve for the second variable. 3. x = 3 – 2y 2x + 6y = -12 4. 3x + y = -5 x – 2y = 3 Solving by Combination: Eliminate one of the variables so that you can solve for the remaining variable. You may have to multiply through one or both equations by a number. 5. x + 3y = 7 -x + y = -3 6. x + 3y = 4 2x – y = 8 If you solve the system and get: x = a number and y = a number then there is one solution and you write it as an ordered pair. (Remember…these are the type of problems we have been working with.) If you graph both you will have two different lines that intersect at one point (the solution). 7. 3x – y = -9 3x + 5y = -15 a true statement such as 0 = 0 or 3 = 3 or –4 = -4, then you have many solutions and you need to write “many solutions”. If you graph both you will end up with the same line. 8. -9x + 9y = 18 3x – 3y = -6 a false statement such as 0 = 4 or 2 = -5, then you have no solutions and you need to write “no solutions”. If you graph both you will end up with two parallel lines. 9. 3x – 4y = -12 y= 3 x–3 4 Graphing Linear Inequalities Think about what type of line to use and where to shade the inequality. 10.) y > ½x + 3 11.) 2x - 3y < -6 Identifying Solutions to a System of Inequalities: Tell whether the ordered pair is a solution to the system of inequalities. (Circle your answer.) 12. 13. 14. Yes- it is a solution Yes- it is a solution Yes- it is a solution No - it is not a solution No - it is not a solution No - it is not a solution Graph the system of inequalities. 15. 17. 19. y 2x 3 y x 1 x0 yx y 2x 3 y 2x 4 16. 18. 20. x 1 2 x 3 y 6 x y 3 y 2x 1 y x3 2 y x 4 Chapter 7 Review Homework 100 Solve the Linear System by Graphing 1. 3 x y 6 2. x y 2 Solve the Linear System by Substitution 3. 5. y 5x 7 4. 4 x y 1 3x y 19 6. x y 7 2 x y 5 x y 1 x y 11 x 3y 1 15 x y 70 3 x 2 y 8 Solve the Linear System by Elimination (Combination) 7. 8 x 3 y 9 8 x y 29 8. x 5 y 3 3 x 5 y 11 9. 4 x y 17 7 y 4x 9 Tell whether the linear system has one solution, no solutions or many solutions. 10. 15 x 3 y 12 y 5x 4 11. 4 x y 4 12. 8 x 2 y 2 Graph the Linear Inequality 13. y 6 14. y 2 x 5 Graph the System of Linear Inequalities 15. 17. y 2x 2 y x 1 x y 6 x y 2 16. 18. y 3x 2 y x4 y 2 2 x 3 y 6 12 x 3 y 18 4 x y 6