Intermediate Algebra (8th Edition)
Intermediate Algebra (8th Edition)
8th Edition
ISBN: 9780134178967
Author: John Tobey Jr., Jeffrey Slater, Jamie Blair, Jenny Crawford
Publisher: PEARSON
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Chapter B, Problem 1E

Solve each system of equations by the matrix method. Round your answers to the nearest tenth when necessary.

2 x + 3 y = 5 5 x + y = 19

Expert Solution & Answer
Check Mark
To determine

To calculate: The values of x and y by the use of the matrix method for the equations, 5x+y=19 and 2x+3y=5.

Answer to Problem 1E

Solution:

The value of x is 4, and the value of y is 1.

Explanation of Solution

Given:

The system of equations is

2x+3y=55x+y=19

Formula Used:

Reduce 2×2 matrix to reduced row echelon form,

[1001]

Calculation:

Consider the equations,

2x+3y=5 …… (1)

5x+y=19 …… (2)

The augmented matrix representation of the equations is,

[2351|519]

The above matrix is converted to therow echelon formwith the help of matrix row operations,

Apply R1R13R2,

[13051|5219]

Apply R2R2+5R113,

[13001|521]

Apply R1R113,

[1001|41]

As the row echelon form is achieved. Thus, the variables are

1(x)+0(y)=4x=4

And,

0(x)+1(y)=1y=1

Hence, the value of x and y are 4 and 1, respectively.

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