Digits, Grade 8, Volume 2, Homework Helper

15-7: TEKS Practice

  • 1. Find the best algebraic method to solve the given system by inspecting the equations.

    table with 2 rows and 2 columns , row1 column 1 , 2 x minus 4 y , column 2 equals negative 2 , row2 column 1 , negative 6 x plus 4 y , column 2 equals negative 14 , end table

    • A. subtraction

    • B. addition

    • C. substitution

  • 2. Which of these systems of equations would be best solved using the subtraction method? Select all that apply.

    • I. table with 2 rows and 2 columns , row1 column 1 , 3 x minus 4 y , column 2 equals 0 , row2 column 1 , negative 9 x plus 4 y , column 2 equals negative 36 , end table

    • II. table with 2 rows and 2 columns , row1 column 1 , 2 y , column 2 equals x minus 2 , row2 column 1 , y , column 2 equals 3 x minus 7 , end table

    • III. table with 2 rows and 2 columns , row1 column 1 , negative 4 x plus 3 y , column 2 equals 0 , row2 column 1 , negative 4 x minus 9 y , column 2 equals negative 36 , end table

    • A. System III

    • B. System II

    • C. System I

  • 3. Which of these systems of equations would be best solved using the subtraction method? Select all that apply.

    • I. table with 2 rows and 2 columns , row1 column 1 , 3 x minus 8 y plus 4 y , column 2 equals negative 2 , row2 column 1 , negative 9 x minus 4 y , column 2 equals negative 50 , end table

    • II. table with 2 rows and 2 columns , row1 column 1 , 2 y , column 2 equals negative 7 x plus 8 x minus 1 , row2 column 1 , y , column 2 equals 3 x minus 7 , end table

    • III. table with 2 rows and 2 columns , row1 column 1 , negative 8 x plus 4 x plus 3 y , column 2 equals negative 2 , row2 column 1 , 4 x minus 9 y , column 2 equals negative 50 , end table

    • A. System I

    • B. System III

    • C. System II

  • 4. Solve the system of equations using subtraction.

    table with 2 rows and 2 columns , row1 column 1 , 2 x minus 7 y , column 2 equals negative 13 , row2 column 1 , 8 x minus 7 y , column 2 equals 11 , end table

  • 5. Solve the system of equations using subtraction.

    table with 2 rows and 2 columns , row1 column 1 , 2 x minus 2 y , column 2 equals negative 4 , row2 column 1 , 2 x plus y , column 2 equals 11 , end table

  • 6. At a basketball game, a team made 56 successful shots. They were a combination of 1- and 2-point shots. The team scored 94 points in all. Write and solve a system of equations to find the number of each type of shot.

  • 7. Yesterday, a movie theater sold 279 bags of popcorn. A large bag of popcorn costs $4. A small bag of popcorn costs $1. In all, the movie theater made $567 from popcorn sales. Write and solve a system of equations to find how many bags of each size of popcorn were sold.

  • 8. 

    • a. Writing Solve the system of equations using subtraction.

      table with 2 rows and 2 columns , row1 column 1 , x plus y , column 2 equals 3 , row2 column 1 , x minus y , column 2 negative 1 , end table

    • b. Describe two different ways to solve the system.

  • 9. 

    • a. Reasoning Which is the best algebraic method to solve the given system by inspecting the equations?

      table with 2 rows and 2 columns , row1 column 1 , 3 x minus 6 y plus 2 y , column 2 equals negative 1 , row2 column 1 , 3 x plus 3 x plus 4 y , column 2 equals 46 , end table

      • A. substitution

      • B. addition

      • C. subtraction

    • b. Explain your reasoning.

  • 10. Error Analysis A student incorrectly claimed the solution of this system of equations is (4, −2).

    table with 2 rows and 2 columns , row1 column 1 , 4 x minus 5 y , column 2 equals 6 , row2 column 1 , 6 x minus 5 y , column 2 equals 14 , end table

    • a. What is the correct solution?

    • b. What mistake might the student have made?

      • A. The signs on the x- and y-coordinates are incorrect.

      • B. The sign on the x-coordinate is correct, but the sign on the y-coordinate is incorrect.

      • C. The student switched the x- and y-coordinates.

      • D. The sign on the y-coordinate is correct, but the sign on the x-coordinate is incorrect.

  • 11. Age If you add Natalie's age and Fred's age, the result is 44. If you add Fred's age to 3 times Natalie's age, the result is 70. Write and solve a system of equations to find how old Fred and Natalie are.


End ofPage 541

Table of Contents

Digits, Grade 8, Volume 2, Homework Helper Unit D: Two-Dimensional Shapes Unit E: Measurement and Data Unit F: Personal Financial Literacy Unit G: Step-Up Lessons English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties