Digits, Grade 8, Volume 2, Homework Helper

#### Part 1

Example Selecting the Most Efficient Method to Solve Systems

Inspect the equations. Decide whether the Addition Method, Subtraction Method, or Substitution Method would be the most efficient algebraic method to solve each system.

table with 3 rows and 3 columns , row1 column 1 , table with 2 rows and 2 columns , row1 column 1 , 5 p plus q , column 2 equals 4 , row2 column 1 , 4 p minus q , column 2 equals 5 , end table , column 2 table with 2 rows and 2 columns , row1 column 1 , y , column 2 equals x plus 3 , row2 column 1 , y , column 2 equals 2 x minus 9 , end table , column 3 table with 2 rows and 2 columns , row1 column 1 , 7 x plus 2 y , column 2 equals 10 , row2 column 1 , 7 x plus y , column 2 equals minus 16 , end table , row3 column 1 , table with 2 rows and 2 columns , row1 column 1 , 2 eh plus 5 b , column 2 equals 17 , row2 column 1 , 6 eh minus 5 b , column 2 equals minus 9 , end table , column 2 table with 2 rows and 2 columns , row1 column 1 , 3 x plus 2 y , column 2 equals 10 , row2 column 1 , x plus 2 y , column 2 equals minus 8 , end table , end table

Solution

In the following two systems, the coefficients of the highlighted terms are additive inverses, so use the addition method.

table with 2 rows and 2 columns , row1 column 1 , 2 a plus 5 b equals 17 , column 2 5 p plus 1 q equals 4 , row2 column 1 , 6 a minus 5 b equals minus 9 , column 2 4 p minus 1 q equals 5 , end table

In the following two systems, the coefficients of the highlighted terms are the same, so use the subtraction method.

table with 2 rows and 4 columns , row1 column 1 , 3 x plus 2 y , column 2 equals 10 , column 3 7 x plus 2 y , column 4 equals 10 , row2 column 1 , x plus 2 y , column 2 equals minus 8 , column 3 7 x plus y , column 4 equals minus 16 , end table

In the system below, the equations are in slope-intercept form, so use the substitution method.

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

#### Part 2

Example Solving a System of Equations by Subtraction

Solve the system by subtraction.

table with 2 rows and 1 column , row1 column 1 , 3 x minus y equals 4 , row2 column 1 , 2 x minus y equals 1 , end table

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