Module Review (RA1 M7) PDF

Student Name: Date: Module Review (RA1 M7) 1) Use the graph. Which system of equations is consistent and dependent? y = 2x + 1 y − 1 = 2x y = 2x + 1 y=3 y=3 x = –2...

Student Name: Date: Module Review (RA1 M7) 1) Use the graph. Which system of equations is consistent and dependent? y = 2x + 1 y − 1 = 2x y = 2x + 1 y=3 y=3 x = –2 x = –2 y + 2 = 2x 2) Fill in the blanks using the available answer choices. Consider the system of equations. 8x + 2y = 8 y = − 4x + 4 The system has solution(s). (Blank 1) Blank 1 options infinitely many no one 3) Tristan is selling plastic and wooden picture frames. He sells 7 frames total. The number of plastic frames Tristan sells is 5 less than twice the number of wooden frames. How many of each type of frame does Tristan sell? wooden frames: sold plastic frames: sold Copyright © 2024, McGraw-Hill Education. 1/9 This content was printed for the exclusive use of licensed students. Student Name: Date: Module Review (RA1 M7) 4) Which shows the system of equations that can be entered into a graphing calculator when solving 3. 5x + 18 = –5. 8x + 30? y = 3. 5x y = –5. 8x y = 3. 5x + 18 y = –5. 8x + 30 0 = 3. 5x + 18 0 = –5. 8x + 30 y = 9. 3x – 12 5) Use a system of equations and a graphing calculator to solve 6. 9x + 4. 3 = –4. 7x + 8. Round to the nearest hundredth, if necessary. x= 6) Match the correct system of equations to each graph and solution. 3x − 6y = 3 4x − 8y = 4 x − 2y = 4 x − 2y = 6 2x − 4y = 8 2x + y = −2 Copyright © 2024, McGraw-Hill Education. 2/9 This content was printed for the exclusive use of licensed students. Student Name: Date: Module Review (RA1 M7) 7) Determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. one solution; (2, 7) one solution; (–2, 7) no solution infinitely many solutions 8) Consider the system of equations. 3x – 2y = 0 3x + 3y = 33 Which expression could be substituted for y in the first equation to find the value of x? –y + 11 –x + 11 1. 5x –3x + 33 Copyright © 2024, McGraw-Hill Education. 3/9 This content was printed for the exclusive use of licensed students. Student Name: Date: Module Review (RA1 M7) 9) Complementary angles are two angles that have measures with a sum of 90°. Angles P and Q are complementary and the measure of angle P is 6° more than twice the measure of angle Q. Write a system of equations and use substitution to find the measures of angles P and Q. 10) Solve the system of equations using substitution. 2r – t = 7 r– t=1 (r, t) = ( , ) 11) True or false: The system of equations has an infinite number of solutions. x + 5y = 2 10y = –2x + 4 True False Copyright © 2024, McGraw-Hill Education. 4/9 This content was printed for the exclusive use of licensed students. Student Name: Date: Module Review (RA1 M7) 12) These systems of equations can be solved using elimination by either adding or subtracting the equations. Sort the systems by their appropriate elimination method for finding their solutions. Elimination Using Elimination Using Addition Subtraction Answer Bank 2f + g = 3 3a + 2b = 5 4x + 3y = 3 6m − 5n = 8 3f − g = 4 a + 2b = 6 − 4x + 2y = 2 − 2m − 5n = 6 13) Three times Mary’s age added to Beth’s age is 34 years. Half of Mary’s age minus Beth’s age is 1 year. How old are Mary and Beth? Mary is years old. Beth is years old. 14) A rectangle is x inches wide and 3y inches long. If the length plus twice the width is 12 inches and the length plus the width is 9 inches, what is the length? 2 in. 3 in. 6 in. 10 in. Copyright © 2024, McGraw-Hill Education. 5/9 This content was printed for the exclusive use of licensed students. Student Name: Date: Module Review (RA1 M7) 15) Select all of the ways the system of equations can be solved. 9x – 2y = 4 3x + 8y = –12 Multiply the second equation by 3, then add the equations. Multiply the first equation by 4, then add the equations. Multiply the first equation by 4, then subtract the equations. Multiply the first equation by 3, then add the equations. Multiply the second equation by 3, then subtract the equations. 16) It takes 3 hours to paddle a kayak 12 miles downstream and 4 hours for the return trip upstream. Find the rate of the kayak in still water. Let k = the rate of the kayak in still water and c = the rate of the current. r t d rt = d Downstream k+c 3 12 3(k + c) = 12 Upstream k−c 4 12 4(k – c) = 12 The rate of the kayak in still water is miles per hour. 17) Solve the system of equations. 2x + 5y = 5 3x + 4y = –3 (x, y) = ( , ) Copyright © 2024, McGraw-Hill Education. 6/9 This content was printed for the exclusive use of licensed students. Student Name: Date: Module Review (RA1 M7) 18) Which graph represents the solution of the system of inequalities? x– y≥2 2x + y > –3 Copyright © 2024, McGraw-Hill Education. 7/9 This content was printed for the exclusive use of licensed students. Student Name: Date: Module Review (RA1 M7) 19) Fill in the blanks using the available answer choices. Dana wants to build a rectangular pen for her goats. The length of the pen should be at least 50 feet, and the perimeter of the pen should be no more than 190 feet. Dana’s goat pen could be wide and long. (Blank 1) (Blank 2) How many different sets of dimensions are possible for this situation? (Blank 3) Blank 1 options Blank 2 options Blank 3 options 29 feet 40 feet one 35 feet 65 feet 140 76 feet infinitely many Copyright © 2024, McGraw-Hill Education. 8/9 This content was printed for the exclusive use of licensed students. Student Name: Date: Module Review (RA1 M7) 20) Fill in the blanks using the available answer choices. The graph shows the solution to the system of inequalities. –x + 2y ≤ 1 − 34 x + 12 y ≥ 12 Solutions to the system of inequalities can be found in the region shaded. (Blank 1) Blank 1 options 1 2 3 4 Copyright © 2024, McGraw-Hill Education. 9/9 This content was printed for the exclusive use of licensed students.