# MATHEMATICS

<object:standard:macc.912.a–rei.3.5>A system of equations is shown below:

x + 3y = 5      (equation 1)

7x – 8y = 6     (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 3x + y = 5 and 8x –7y = 6 is the same as the solution to the given system of equations Show that the solution to the system of equations 8x – 5y = 11 and 7x – 8y = 6 is the same as the solution to the given system of equations Show that the solution to the system of equations 15x + 13y = 17 and 7x – 8y = 6 is the same as the solution to the given system of equations Show that the solution to the system of equations –13x + 15y = 17 and 7x – 8y = 6 is the same as the solution to the given system of equations

#### Question 2

(05.02)<object:standard:macc.912.a–rei.3.6>

Solve the following system of equations:

3x – 2y = 6

6x – 4y = 12

(0, 0) (6, 12) Infinitely many solutions No solutions

#### Question 3

(05.01)<object:standard:macc.912.a–rei.3.6>

Which graph below shows a system of equations with infinitely many solutions?

#### Question 4

(05.02)<object:standard:macc.912.a–rei.3.6>

A system of equations is shown below:

x + y = 3

2x – y = 6

The x-coordinate of the solution to this system of equations is _____.

#### Question 5

(05.01)<object:standard:macc.912.a–rei.3.6>

The two lines, X and Y, are graphed below:

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 6

(05.06)<object:standard:macc.912.a–ced.1.3>

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  20

15t + 8b = 150 t + b  20

15t + 8b  150 t + b  20

15t + 8b  150 None of the systems shown represent this scenario.

#### Question 7

(05.02)<object:standard:macc.912.a–rei.3.5>

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 8

(05.06)<object:standard:macc.912.a–rei.4.12>

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?

#### Question 9

(05.02)<object:standard:macc.912.a–rei.3.6>

The total price of a shirt and a cap is \$11. If the price of the shirt was doubled and the price of the cap was 3 times its original price, the total price of a shirt and a cap would be \$25. What is the price of a shirt and a cap?

The price of a shirt is \$9, and the price of a cap is \$2. The price of a shirt is \$10, and the price of a cap is \$1. The price of a shirt is \$8, and the price of a cap is \$3. The price of a shirt is \$7, and the price of a cap is \$4.

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