Digits, Grade 8, Volume 2, Homework Helper

### 15-6: TEKS Practice

• 1. Find the most efficient algebraic method to solve each system of equations.

• I. table with 2 rows and 2 columns , row1 column 1 , negative 2 x plus 5 y , column 2 equals 10 , row2 column 1 , 5 x minus 5 y , column 2 equals minus 10 , end table

• II. table with 2 rows and 2 columns , row1 column 1 , y , column 2 equals 2 x plus 10 , row2 column 1 , 5 x minus 5 y , column 2 equals minus 10 , end table

• 2. Which system of equations is best solved using addition?

• A. table with 2 rows and 2 columns , row1 column 1 , negative 3 x plus 5 y , column 2 equals 9 , row2 column 1 , 3 x minus 2 y , column 2 equals minus 9 , end table

• B. table with 2 rows and 2 columns , row1 column 1 , x , column 2 equals 5 y plus 9 , row2 column 1 , negative 3 x minus 2 y , column 2 equals minus 9 , end table

• C. table with 2 rows and 2 columns , row1 column 1 , x , column 2 equals 5 y plus 9 , row2 column 1 , negative 3 x minus 2 y , column 2 equals 9 , end table

• 3. Solve the system of equations using addition.

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

• 4. Which systems of equations are best solved using addition? Select all that apply.

• A. table with 2 rows and 2 columns , row1 column 1 , x , column 2 equals minus 3 y plus 9 , row2 column 1 , 5.1 x minus 5.1 y , column 2 equals 9 , end table

• B. table with 2 rows and 2 columns , row1 column 1 , 5.1 x plus 5.1 y , column 2 equals 9 , row2 column 1 , 5.1 x minus 5.1 y , column 2 equals minus 9 , end table

• C. table with 2 rows and 2 columns , row1 column 1 , 3 x plus 3 y , column 2 equals 9 , row2 column 1 , negative 3 x minus 5 y , column 2 equals minus 9 , end table

• D. table with 2 rows and 2 columns , row1 column 1 , x , column 2 equals 3 y plus 9 , row2 column 1 , 3 x minus 5 y , column 2 equals minus 9 , end table

• 5. Think About the Process Suni needs to solve the system of equations using addition.

table with 2 rows and 2 columns , row1 column 1 , negative 5 x plus 3 y , column 2 equals 15 , row2 column 1 , 2 x minus 3 y , column 2 equals minus 15 , end table

• a. What variable should Suni solve for first?

• A. y

• B. x

• b. Find the solution.

• 6. Solve the system using addition.

table with 2 rows and 2 columns , row1 column 1 , 7 x plus 2 y , column 2 equals minus 13 , row2 column 1 , negative 7 x plus y , column 2 equals 25 , end table

• 7. Think About the Process Two friends spent \$47 at the mall. The first friend spent less than the second friend. The difference between the amount each friend spent was \$31. To find the amount each friend spent, solve a system of equations using the addition method.

• a. What is the next step after writing the system of equations?

• A. Graph the system of equations.

• B. Add the equations to eliminate a variable.

• C. Solve one of the equations for one of the variables.

• D. Substitute an expression for one of the variables into the other equation.

• b. Find the amount each friend spent.

• 8. The sum of two numbers is 23. When the second number is subtracted from the first number, the difference is 9. Find the two numbers.

• 9. There are two red jars of marbles and one blue jar of marbles. Jars of the same color marbles contain the same number of marbles in them. There are 35 marbles in total. The difference between the number of marbles in a red jar and the number of marbles in a blue jar is 4. Find the number of marbles in each type of jar.

• 10.

• a. Writing Solve the system using addition.

table with 2 rows and 2 columns , row1 column 1 , x minus 3.1 y , column 2 equals , 11.5 , row2 column 1 , negative x plus 3.5 y , column 2 equals minus , 13.5 , end table

• b. Explain why the addition method is a good choice for solving the system. If you wanted to solve for x first, is the addition method still a good choice? Explain.

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