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

• 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

• C. subtraction

• 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.

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