anonymous
  • anonymous
5x + 2y = 3 (equation 1) 2x − 3y = 1 (equation 2) A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof? Show that the solution to the system of equations 7x − y = 4 and 2x − 3y = 1 is the same as the solution to the given system of equations Show that the
Mathematics
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chestercat
  • chestercat
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anonymous
  • anonymous
A system of equations is shown below: 5x + 2y = 3 (equation 1) 2x − 3y = 1 (equation 2) A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof? Show that the solution to the system of equations 7x − y = 4 and 2x − 3y = 1 is the same as the solution to the given system of equations Show that the solution to the system of equations 2x + 5y = 3 and 3x − 2y = 1 is the same as the solution to the given system of equations Show that the solution to the system of equations 9x + 4y = 5 and 7x − y = 4 is the same as the solution to the given system of equations Show that the solution to the system of equations −4x + 9y = 5 and 2x − 3y = 1 is the same as the solution to the given system of equations Question 4 (Multiple Choice Worth 4 points) (05.03) Which of the following statements best describes the graph of −5x + 2y = 1? It is a curve joining the points (−5, 2), (2, 3), and (4, 1). It is a curve joining the points (−1, −3), (−1, −3), and (1, 5). It is a straight line joining the points (1, 3), (3, 8), and (−3, −7). It is a straight line joining the points (4, −3), (−1, 2), and (−4, 5). Question 5 (Fill-In-The-Blank Worth 4 points) (05.02) A system of equations is shown below: 6x − 5y = 5 3x + 5y = 4 The x-coordinate of the solution to this system of equations is _____. Numerical Answers Expected! Answer for Blank 1: Question 6 (Multiple Choice Worth 4 points) (05.03) The graph of an equation is shown below: line joining ordered pairs negative 2, negative 3 and 2,3 Based on the graph, which of the following represents a solution to the equation? (−2,−3) (2, 1) (1, 2) (−3, −2) Question 7 (Multiple Choice Worth 4 points) (05.03) The graph below shows two functions: function f of x is a straight line which joins the ordered pairs negative 2.5, 9 and 2.5, negative 1. Function g of x is a curved line which joins the ordered pairs negative 1.4, 6.8 and 2, 0.2 Based on the graph, what are the approximate solutions to the equation −2x + 4 = (0.25)x? −1.4 and 2 1.4 and −2 4 and 2 1 and 4 Question 8 (Multiple Choice Worth 5 points) (05.05) Greg has only nickels and dimes in his money box. He knows that he has more than $10 in the box. Let x represent the number of nickels in the box and y represent the number of dimes in the box. Which of the following statements best describes the steps to graph the solution to the inequality in x and y? Draw a dashed line to represent the graph of 5x + 10y = 1000, and shade the portion below the line for positive values of x and y. Draw a dashed line to represent the graph of 5x + 10y = 1000, and shade the portion above the line for positive values of x and y. Draw a dashed line to represent the graph of 10x + 5y = 1000, and shade the portion above the line for positive values of x and y. Draw a dashed line to represent the graph of 10x + 5y = 1000, and shade the portion below the line for positive values of x and y. Question 9 (Multiple Choice Worth 4 points) (05.02) Sam and Harry are family. Sam is currently is three times Harry's age. Sam's age is also 10 more than twice Henry's age. What are their current ages? Sam is 24 years old, and Harry is 8 years old. Sam is 39 years old, and Harry is 13 years old. Sam is 27 years old, and Harry is 9 years old. Sam is 30 years old, and Harry is 10 years old. Question 10 (Multiple Choice Worth 5 points) (05.06) A system of linear inequalities is shown below: y − x > 0 x + 1 < 0 Which of the following graphs best represents the solution set to this system of linear inequalities? The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 4, 4. The portion common to the right of the first line and above the second line is shaded The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 2, 2. The portion common to the left of the first line and above the second line is shaded The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 2, 2. The portion common to the left of the first line, above the second line and below the x axis is shaded The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 3, 3. The portion common to the left of the first line and above the x axis is shaded Question 11 (Multiple Choice Worth 4 points) (05.01) A pair of linear equations is shown below: y = −2x + 3 y = −4x − 1 Which of the following statements best explains the steps to solve the pair of equations graphically? Graph the first equation, which has slope = 3 and y-intercept = −2, graph the second equation, which has slope = −1 and y-intercept = −4, and find the point of intersection of the two lines. Graph the first equation, which has slope = −3 and y-intercept = 2, graph the second equation, which has slope = 1 and y-intercept = 4, and find the point of intersection of the two lines. Graph the first equation, which has slope = −2 and y-intercept = 3, graph the second equation, which has slope = −4 and y-intercept = −1, and find the point of intersection of the two lines. Graph the first equation, which has slope = 2 and y-intercept = −3, graph the second equation, which has slope = 4 and y-intercept = 1, and find the point of intersection of the two lines. Question 12 (Multiple Choice Worth 5 points) (05.02) For the following system, if you isolated x in the first equation to use the Substitution Method, what expression would you substitute into the second equation? −x + 2y = −6 3x + y = 8 −2y + 6 2y − 6 2y + 6 −2y − 6 Question 13 (Multiple Choice Worth 4 points) (05.03) An equation is shown below: 2 over 3 multiplied by x plus 8 over 3 equals 2 to the power of x What is the solution to the equation? x = −2 x = −1 x = 1 x = 2 Question 14 (Multiple Choice Worth 5 points) (05.06) Look at the graph below: First line joins ordered pairs negative 4, 3 and 2, negative 3. Second line joins negative 4, negative 3 and 2, 3. Part A shaded above first and second line. Part B shaded below first line and above second line. Part C shaded below first and second lines. Part D shaded above first line and below second line. Which part of the graph best represents the solution set to the system of inequalities y ≥ x + 1 and y + x ≥ −1? Part A Part B Part C Part D Question 15 (Multiple Choice Worth 4 points) (05.01) The two lines, X and Y, are graphed below: Line X is drawn by joining ordered pairs negative 3,12 and 7,negative 16. Line Y is drawn by joining ordered pairs 0, negative 14 and 11, 8 Determine the solution and the reasoning that justifies the solution to the systems of equations. (2, 7), because this point is true for both the equations (4, −6), because this point lies only on one of the two lines (4, −6), because this point makes both the equations true (2, 7), because the lines intersect the x-axis at these points Question 16 (Multiple Choice Worth 5 points) (05.01) Which graph below shows a system of equations with one solution? coordinate plane with two parallel lines coordinate plane with two intersecting lines coordinate plane with two coinciding lines coordinate plane with two parallel lines Question 17 (Multiple Choice Worth 4 points) (05.05) Midge baked 6 cookies and 4 brownies. Midge only has enough ingredients to bake at most 25 cookies or brownies total. Let x represent the number of more cookies and y represent the number of more brownies that Midge can bake. Which of the following graphs best represents the relationship between x and y? line joining ordered pair 0, 15 and 7, 8 and the region below this line which lies in the first quadrant is shaded line joining ordered pair 0, 25 and 7, 18 and the region below this line which lies in the first quadrant is shaded line joining ordered pair 10, 0 and 0, 10 and the region below this line which lies in the first quadrant is shaded line joining ordered pair 0, 6 and 4, 0 and the region below this line which lies in the first quadrant is shaded Question 18 (Multiple Choice Worth 5 points) (05.02) Two systems of equations are shown below: System A System B 2x + y = 5 −10x + 19y = −1 −4x + 6y = −2 −4x + 6y = −2 Which of the following statements is correct about the two systems of equations? They will have the same solutions because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A. They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A. The value of x for System B will be −5 times the value of x for System A because the coefficient of x in the first equation of System B is −5 times the coefficient of x in the first equation of System A. The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −12 to the first equation of System A and the second equations are identical. Question 19 (Multiple Choice Worth 4 points) (05.01) The graph plots four equations, A, B, C, and D: Line A joins ordered pair negative 6, 16 and 9, negative 4. Line B joins ordered pair negative 2, 20 and 8, 0. Line C joins ordered pair negative 7, negative 6 and 6, 20. Line D joins ordered pair 7, 20 and 0, negative 7. Which pair of equations has (0, 8) as its solution? Equation A and Equation C Equation B and Equation C Equation C and Equation D Equation B and Equation D Question 20 (Multiple Choice Worth 5 points) (05.06) Nick works two jobs to pay for college. He tutors for $15 per hour and also works as a bag boy for $8 per hour. Due to his class and study schedule, Nick is only able to work up to 20 hours per week but must earn at least $150 per week. If t represents the number of hours Nick tutors and b represents the number of hours he works as a bag boy, which system of inequalities represents this scenario? t + b greater than or equal to 20 15t + 8b = 150 t + b less than or equal to 20 15t + 8b greater than or equal to 150 t + b less than or equal to 20 15t + 8b less than or equal to 150 None of the systems shown represent this scenario. Question 21 (Multiple Choice Worth 4 points) (05.05) A graph is shown below: Dotted line joining negative 1, negative 2 and 5,0 and the region above the line is shaded. Which of the following inequalities is best represented by this graph? x − 3y > 5 x − 3y < 5 x − 2y > 5 x − 2y < 5 Question 22 (Multiple Choice Worth 4 points) (05.03) The tables below show the values of f(x) and g(x) for different values of x: f(x) = 2(3)x x f(x) −2 0.22 −1 0.67 0 2 1 6 2 18 g(x) = 3x + 3 x g(x) −2 3.11 −1 3.33 0 4 1 6 2 12 Based on the tables, what is the solution to the equation 2(3)x = 3x + 3? x = −1 x = 0 x = 1 x = 6 Question 23 (Multiple Choice Worth 4 points) (05.02) Maya had $27. She spent all the money on buying 3 burgers for $x each and 2 sandwiches for $y each. If Maya had bought 2 burgers and 1 sandwich, she would have been left with $11. A student concluded that the price of each burger is $5 and the price of each sandwich is $6. Which statement best justifies whether the student's conclusion is correct or incorrect? The student's conclusion is correct because the solution to the system of equations 3x + 2y = 11 and 2x + y = 16 is (5, 6). The student's conclusion is incorrect because the solution to the system of equations 3x − 2y = 11 and 2x − y = 16 is (5, 6). The student's conclusion is correct because the solution to the system of equations 3x + 2y = 27 and 2x + y = 16 is (5, 6). The student's conclusion is incorrect because the solution to the system of equations 2x + 3y = 27 and x + 2y = 16 is (5, 6). You must check the box below prior to submitting your exam! Check this box to indicate you are ready to submit your exam Submit Exam Help Explorer Toolbox Workload My Folders Current course: Related Help Center Topics Taking Exams Proctored Exams Question Types Educator ®
anonymous
  • anonymous
Help me plz
Frozen15
  • Frozen15
I can help you on your first one .. your answer is Show that the solution to the system of equations 7x – y = 4 and 2x – 3y = 1 is the same as the solution to the given system of equations

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anonymous
  • anonymous
Maybe you should ask your questions 1 at a time.
Frozen15
  • Frozen15
I agree with @odayin , you shouldn't smush 20 questions at a time

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