Beginning & Intermediate Algebra (6th Edition)
Beginning & Intermediate Algebra (6th Edition)
6th Edition
ISBN: 9780134193090
Author: Elayn Martin-Gay
Publisher: PEARSON
Question
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Chapter D, Problem 1P
To determine

To find:

The solutions of the system of equations.

x+4y=-2

3x-y=7

Expert Solution & Answer
Check Mark

Answer to Problem 1P

Solution:

x=2;y=-1

Explanation of Solution

1) Concept:

To solve a system of two equations in x and y using matrices:

Step 1. Write the corresponding matrix associated with the system of equations.

Step 2. Use elementary row operations to get equivalent matrix of the form:

1a01bc; where a,b,c are constants.

Step 3. Solve for x and y.

2) Calculation:

x+4y=-2

3x-y=7

The corresponding matrix associated with the above system of equations is

143-1-27

The element in (row1, column1) position is already 1.

To get the (row2, column1) position as zero, multiply row1 by -3 and add to row2:

14-31+3-34-1-2-3-2+7

Simplify further:

140-13-213

Use elementary row operation to get the (row2, column2) position as 1.

So, divide row 2 by -13

140-13-13-13-213-13

Simplify further,

1401-2-1

The above matrix corresponds to the system of equations:

x+4y=-2

y=-1

Substitute y=-1 in the first equation, x+4y=-2.

x+4-1=-2

x-4=-2

x=-2+4

x=2

Thus, the solutions of the given system of equations are: x=2;y=-1.

Conclusion:

Therefore, the required solutions are: x=2;y=-1.

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