6 which of the following equations would give you a system of equations with the same line and infinitely many solutions?

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1 Algebra Worksheet Name: Per: Part I: Solve each system of equations using the graphing method. 1) y = x 5 ) -x + y = 6 y = x + 1 y = -x 3) y = 1 x 3 4) 4x y = 8 y = 1 x + 1 y = x + 3 5) x + y = 6 6) x = -3 y = -x + 6 y = 7) Given the equation x y 6 which of the following equations would give you a system of equations with the same line and infinitely many solutions? A. y x 3 C. y x 4 B. y 0.5x 3 D y x 3 8) Given the equation y = 3x 5, which of the following equations would give you a system of equations with parallel lines and no solution? A. y = -3x + C. y = 5x 3 B. y = 3x + 4 D. y = -5x + 9) A system of two linear equations has one solution. What must be true about the lines? A) They are parallel. B) They are perpendicular. C) They are the same line. D) They intersect.

2 10) The functions f(x) and g(x) are graphed to the side. Approximate the value x whenf(x) = g(x)? a) x =.5 b) x = 0.9 c) x = 3.5 d) x = 1 11) How many solutions will the following system of equations have? Support your conclusion with a written explanation of your thoughts. { y = 1 x 3 y = x + 1 1) Solve the following system of equations by graphing, and then explain why this problem is difficult to solve by graphing. y = 3x 4 { y = 5x + 1 For #13 14: A pet store sells angel fish for $6 each and clown fish for $4 each. If the pet store sold five fish for a total of $4, how many of each type of fish were sold? 13) Write two equations to model this situation. 14) Solve the system by graphing. Angel fish = Clown fish = 15) Which equation would make this system have an infinite number of solutions? y = x + { A. y = x + 4 C. y = x B. y x = 3 D. y = 3x 1

3 Algebra 1 Name: Per: 4-3 Day 1 Worksheet Do all work on your own paper! Show all work! Part I: Use the elimination method to solve each system of equations. Show all work! 1) x + y = 13 ) -3x 5y = -7 -x + y =5-4x + 5y = 14 3) x + y = 1 4) y = x + 4 x + y = 1 x + 3y = 4 5) 1 x y = 7 6) 0.5x 0.10y = x + y = 4 0.5x 0.0y = ) 9y = -4x - 8) -11y = -3x 18 11x + 9y = 6 16y 3x = 33 9) Two brothers Jason and Michael couldn t decide if they wanted to take their kids to McDonalds or Burger King for their soccer team s win. Jason took his children to McDonald s, where it was $3 per hamburger and $3 per French fries. He spent $4. Michael took his children to Burger King, where it was $3 per hamburger, but $ for the fries. He spent $0. If they both purchased the same amount of burgers and fries, how many did they buy of each? Show all of your work. 10) Jenny and Bob are competing with one another to see who can sell the most cookies and wrapping paper for their school s fundraiser. Jenny s grade is selling wrapping paper for $10 per roll and cookies for $3 per bucket. She ended up making $165 total. Bob s grade is selling the wrapping paper for $10 and a bucket of gourmet cookies for $7 per bucket. He ended up making $185 total. If they tied and sold the same amount of wrapping paper and cookies, how many of each did they sell? 11) Graph y = -x + 4 1) An apple orchard allows people to come and pick their own apples. Customers pay $5 for a basket and $0.10 for each apple. The function f(x) = 0.10x + 5 gives the cost for x apples picked. What is the range of the function? A. {all real numbers} C. {0, 0.10, 0.0, 0.30, 0.40, 0.50 } B. {0, 1,, 3, 4, 5 } D. {5, 5.10, 5.0, 5.30, 5.40, 5.50 } More on the back

4 13) The graph below shows the account balance of a student s lunch money account. Which of the following statements are true? Select all that apply. F. Each lunch costs $4. G. Each lunch costs $5. H. The account started with a balance of $40. I. The student won t have any money left in the account after eating 8 lunches. J. The student has enough money in the account to pay for 40 lunches. Bonus: A line graphed on the coordinate plane has a slope of and contains the point (3, 1). Which of the following points is on the same line? A. ( 3, 5) C. (0, 5) B. ( 3, ) D. ( 5, 0)

5 Algebra 1 Name: Per: 4 3 Day Worksheet Do all work on your own paper. Show all work! For #1 6: Solve the linear system. 1) x + y = ) 4x + 1y = 8 x + 7y = 9 x + 3y = 3) 11x 0y = 8 4) 1x 7y = - 3x + 4y = 36-8x + 11y = 14 5) x + y = 9 6) 15x + 8y = x + 0.5y = x + 1y = 14 7) A group of 30 students from the senior class charters a bus to an amusement park. The total amount they spend on the bus and admission to the park for each student is $1,770. A group of 50 students from the junior class also go the amusement park, but they require two buses. If the group from the junior class spent $3,190 in total, how much does it cost to charter one bus? 8) Tickets for admission to a high school football game cost $3 for students and $5 for adults. During one game, $995 was collected from the sale of 79 tickets. How many adult tickets and student tickets were sold? 3x y = 5 9) Given the system { which of the following ordered pairs is a solution? x + 3y = 38 A) (4, 9) B) (7, 8) C) (11, -3) D) (-5, 10) 10) Write the equation of a line (in slope-intercept form) that passes through (, 5) and (-1, 8). 11) If h(x) = 1 x + 3, find h( 7). A. B C. 60 D. 7 x The equations of four lines are given below. Which two equations form a system with no solutions? A. Line 1 and Line B. Line and Line 3 C. Line and Line 4 D. Line 1 and Line 3 Line 1 x 3y = 9 Line y = (x + 1) 7 Line 3 y = 1 3 x + Line 4 y = 1 (x 4) 1 More on the back

6 13. The graph and a table of values are given to represent two linear equations in a system of equations. Which of the following is the solution to the system? Line A Line B x y A. (, 0) B. (0, 3) C. ( 1, 5) D. (, 6)

7 Algebra Worksheet Name For #1 3: Determine whether the ordered pair is a solution of the inequality. (Yes or no, show work for credit) 1. x + y > 9 ; (0,0). x y 8 ; (14,9) 3. x y > 4 ; ( 6, 15) For #4 6: Match each linear inequality to its graph. 4) y < x + 5 5) x y 4 6) 3y 6x 1 A) B) C) For #7 1: Graph the inequality. (Show work for credit) 7. y < x x y < 4 9. y < 1 x y 10x y 1 18x 1. (y + 3) > 4x 13. (x y) x y > 7

8 For #13 15: Graph the inequality. (Show work for credit) 13. 5y x x + 3 > 4 For #16 18: A soccer team holds a banquet at the end of the season. 16) The team needs to seat at least 96 people and plans to use two different-sized tables. A small table can seat 6 people, and a large table can seat 8 people. Write a linear inequality that represents the numbers of each size table the team needs. Let x = # of small tables and let y = # of large tables. 17) Graph your inequality from #16. 18) If the school has 5 small tables and 9 large tables, will this be enough for the banquet? 19) Basketball player Dwight Howard wants to score at least 5 points in a playoff game. His coach has instructed him that he cannot take any 3-point shots. He can attempt to make a field goal, which is worth points each time, or a free throw shot, which is worth 1 point each time. Let x represent the number of field goals he makes, and let y represent the number of free throws he makes. Write and graph an inequality that models the different number of field goals and free throws he can make to score at least 5 points. Bonus: Write an equation, in (h, k) form, of the line passes through the points ( 1, 6) and ( 5, 9).