   # Further Investigations A system such as ( 3 x + 2 y = 2 2 x − 3 y = 1 4 ) is not a system of linear equations nut can be transformed into a linear system by changing variables. For example, when we substitute u for 1 x and v for 1 y , the system cited becomes ( 3 u + 2 v = 2 2 u − 3 v = 1 4 ) We can solve this “new” system either by elimination by addition or by substitution (we will leave the details for you) to produce u = 1 2 and v = 1 4 . Therefore, because u = 1 x and v = 1 y , we have 1 x = 1 2 and 1 y = 1 4 Solving these equations yields, x = 2 and y = 4 The solution set of the original system is { ( 2 , 4 ) } . Solve each of the following system. (a) ( 1 x + 2 y = 7 12 3 x − 2 y = 5 12 ) (b) ( 2 x + 3 y = 19 15 − 2 x + 1 y = − 7 15 ) (c) ( 3 x − 2 y = 13 6 2 x + 3 y = 0 ) (d) ( 4 x + 1 y = 11 3 x − 5 y = − 9 ) (e) ( 5 x − 2 y = 23 4 x + 3 y = 23 2 ) (f) ( 2 x − 7 y = 9 10 5 x + 4 y = − 41 20 ) ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728

#### Solutions

Chapter
Section ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter 10.3, Problem 65PS
Textbook Problem
1 views

## Further InvestigationsA system such as ( 3 x + 2 y = 2 2 x − 3 y = 1 4 ) is not a system of linear equations nut can be transformed into a linear system by changing variables. For example, when we substitute u for 1 x and v for 1 y , the system cited becomes ( 3 u + 2 v = 2 2 u − 3 v = 1 4 ) We can solve this “new” system either by elimination by addition or by substitution (we will leave the details for you) to produce u = 1 2 and v = 1 4 . Therefore, because u = 1 x and v = 1 y , we have 1 x = 1 2 and 1 y = 1 4 Solving these equations yields, x = 2 and y = 4 The solution set of the original system is { ( 2 , 4 ) } . Solve each of the following system. (a) ( 1 x + 2 y = 7 12 3 x − 2 y = 5 12 ) (b) ( 2 x + 3 y = 19 15 − 2 x + 1 y = − 7 15 ) (c) ( 3 x − 2 y = 13 6 2 x + 3 y = 0 ) (d) ( 4 x + 1 y = 11 3 x − 5 y = − 9 ) (e) ( 5 x − 2 y = 23 4 x + 3 y = 23 2 ) (f) ( 2 x − 7 y = 9 10 5 x + 4 y = − 41 20 )

To determine

a)

To solve:

The following system.

### Explanation of Solution

Approach:

To convert the given system into system of linear equations,

Let’s substitute u for 1x and v for 1y.

Given:

(1x+2y=7123x2y=512)

Calculation:

The new system is,

(u+2v=7123u2v=512)

To solve this system, we will simplify the equations,

u+2v=712 can be simplified to 12u+24v=73u2v=512can be simplified to 36u24v=5

As the coefficients of variable v are same in both the equations, we will use the elimination-by-addition method

To determine

b)

To solve:

The following system.

To determine

c)

To solve:

The following system.

To determine

d)

To solve:

The following system.

To determine

e)

To solve:

The following system.

To determine

f)

To solve:

The following system.

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