Use the graph to determine whether each system is consistent or inconsistent and if it is independent or dependent.


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1 Use the graph to determine whether each system is consistent or inconsistent and if it is independent or dependent. y = 2x 1 y = 2x + 3 The lines y = 2x 1 and y = 2x + 3 intersect at exactly one point which means this system has exactly one solution. So, the system is consistent and independent. y = 2x + 3 y = 2x 3 The lines y = 2x + 3 and y = 2x 3 never intersect which means this system has no solution. So, the system is inconsistent. esolutions Manual  Powered by Cognero Page 1
2 Graph each system and determine the number of solutions that it has. If it has one solution, name it. y = 2x 3 y = x + 4 y = 2x 3 y = x + 4 The graphs appear to intersect at the point (7, 11). You can check this by substituting 7 for x and 11 for y. The solution is (7, 11). esolutions Manual  Powered by Cognero Page 2
3 x + y = 6 x y = 4 To graph the system, write both equations in slopeintercept form. y = x + 6 y = x 4 The graphs appear to intersect at the point (5, 1). You can check this by substituting 5 for x and 1 for y. The solution is (5, 1). x + y = 8 3x + 3y = 24 To graph the system, write both equations in slopeintercept form. y = x + 8 y = x + 8 When written in slopeintercept form, you can see that the equations represent the same line. There are an infinite number of solutions. esolutions Manual  Powered by Cognero Page 3
4 x 4y = 6 y = 1 To graph the system, write both equations in slopeintercept form. Graph and y = 1. The graphs appear to intersect at the point (10, 1). You can check this by substituting 10 for x and 1 for y. The solution is (10, 1) = 12 esolutions Manual  Powered by Cognero Page 4
5 3x + 2y = 12 3x + 2y = 6 To graph the system, write both equations in slopeintercept form. Graph and. The lines are parallel. So, there is no solution. esolutions Manual  Powered by Cognero Page 5
6 2x + y = 4 5x + 3y = 6 To graph the system, write both equations in slopeintercept form. Equation 1: Equation 2: Graph y = 2x 4 and. The graphs appear to intersect at the point (6, 8). You can check this by substituting 6 for x and 8 for y. The solution is (6, 8). esolutions Manual  Powered by Cognero Page 6
7 Use substitution to solve each system of equations. y = x + 4 2x + y = 16 y = x + 4 2x + y = 16 Substitute x + 4 for y in the second equation. Use the solution for x and either equation to find the value for y. The solution is (4, 8). y = 2x 3 x + y = 9 y = 2x 3 x + y = 9 Substitute 2x 3 for y in the second equation. Use the solution for x and either equation to find the value for y. The solution is (12, 21). esolutions Manual  Powered by Cognero Page 7
8 x + y = 6 x y = 8 x + y = 6 x y = 8 Solve the first equation for x. Substitute 6 y for x in the second equation. Use the solution for y and either equation to find the value for x. The solution is (7, 1). y = 4x 6x y = 30 y = 4x 6x y = 30 Substitute 4x for y in the second equation. Use the solution for x and either equation to find the value for y. The solution is (3, 12). esolutions Manual  Powered by Cognero Page 8
9 The cost of two meals at a restaurant is shown in the table. Define variables to represent the cost of a taco and the cost of a burrito. Write a system of equations to find the cost of a single taco and a single burrito. Solve the systems of equations, and explain what the solution means. How much would a customer pay for 2 tacos and 2 burritos? Let t = the cost of a taco and b = the cost of a burrito. The cost of a meal with 3 tacos and 2 burritos is $7.40. So, 3t + 2b = 7.4. The cost of a meal with 4 tacos and 1 burrito is $6.45. So, 4t + b = c. 3t + 2b = 7.4 4t + b = 6.45 Solve the second equation for b. Substitute 4t for b in the first equation. Use the solution for t in either equation to find the value of b. The cost of a single taco is $1.10 and the cost of a single burrito is $2.05. d. Substitute these values into the equation to find how much a customer pays for 2 tacos and 2 burritos. esolutions Manual  Powered by Cognero Page 9
10 A customer would pay $6.30 for 2 tacos and 2 burritos. The cost of two groups going to an amusement park is shown in the table. Define variables to represent the cost of an adult ticket and the cost of a child ticket. Write a system of equations to find the cost of an adult and child admission. Solve the system of equations, and explain what the solution means. d. Let a = cost of an adult ticket and c = the cost of a child ticket. The cost of a group with 4 adults and 2 children is $184. So, 4a + 2c = 184. The cost of a group with 4 adults and 3 children is $200. So, 4a + 3c = 200. Notice that the coefficients of the a terms are the same, so subtract the equations. Use the solution for c in either equation to find the value of a. The cost of an adults ticket is $38, and the cost of a childs ticket is $16. Substitute these values into the equation to find the total cost of admission. A group of 3 adults and 5 children visiting the amusement park will be charged $194 for admission. Angelina spends $16 for 12 pieces of candy to take to a meeting. Each chocolate bar esolutions Manual  Powered by Cognero Page 10
11 Angelina spends $16 for 12 pieces of candy to take to a meeting. Each chocolate bar costs $2, and each lollipop costs $1. Determine how many of each she bought. 6 chocolate bars, 6 lollipops 4 chocolate bars, 8 lollipops 7 chocolate bars, 5 lollipops 3 chocolate bars, 9 lollipops Let c = the number of chocolate bars and = the number of lollipops. Angelina buys 12 pieces of candy. So, c + = 12. She spends $16. So, 2c + 1 = 16. Since both equations contain, use elimination by subtraction. Substitute 4 for c in either equation to solve for. So, B is the correct choice. esolutions Manual  Powered by Cognero Page 11
12 Use elimination to solve each system of equations. x + y = 9 x y = 3 Because y and y have opposite coefficients, add the equations. Now, substitute 3 for x in either equation to find the value of y. The solution is (3, 6). x + 3y = 11 x + 7y = 19 Because x and x have the same coefficients, subtract the equations. Now, substitute 2 for y in either equation to find the value of x. The solution is (5, 2). esolutions Manual  Powered by Cognero Page 12
13 9x 24y = 6 3x + 4y = 10 Multiply each term in the second equation by 3 to eliminate the x coefficient. Because 9x and 9x have opposite coefficients, add the equations. Now, substitute 1 for y in either equation to find the value of y. The solution is (2, 1). 5x + 2y = 11 5x 7y = 1 Because 5x and 5x have opposite coefficients, add the equations. Now, substitute 2 for y in either equation to find the value of x. The solution is (3, 2). The Blue Mountain High School Drama Club is selling tickets to their spring musical. esolutions Manual  Powered by Cognero Page 13
14 The Blue Mountain High School Drama Club is selling tickets to their spring musical. Adult tickets are $4 and student tickets are $1. A total of 285 tickets are sold for $765. How many of each type of ticket are sold? 145 adult, 140 student 120 adult, 165 student 180 adult, 105 student 160 adult, 125 student Let a = the number of adult tickets sold and s = the number of student tickets sold. So, a + s = 285 and 4a + 1s = 765. Solve the first equation for s. Substitute 285 a for s in the second equation. Use the solution for a in either equation to find the value of s. So, J is the correct choice. esolutions Manual  Powered by Cognero Page 14
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