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Chapter 4: Q 4.81 (page 438)

Solve the system of equations using a matrix:2x+y=7x-2y=6

Short Answer

Expert verified

The solution for the system of linear equation is4,-1.

Step by step solution

01

Step 1. Given information.

Consider the given system of equations,

2x+y=7x-2y=6

02

Step 2. Write in augmented form.

The augmented matrix for the given system of equations is

2171-26

03

Step 3. Apply row operations.

Apply R12鈫�R1,

112720-26

Apply R2-R1鈫�R2,

112720-5252

Apply -25脳R2鈫�R2,

1127201-1

Now, the matrix is in row-echelon form.

04

Step 4. Write in system of equations.

Writing the corresponding system of equations,

x+12y=72......(i)y=-1......(ii)

Substitute yin equation (i),

x+12-1=72x=72+12x=82x=4

05

Step 5. Check the answers.

Substitute the values x,yin equation (i),

4+12-1=724-12=7272=72

This is true.

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