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Chapter 4: Q. 4.82 (page 438)

Solve the system of equations using a matrix:2x+y=-4x-y=-2

Short Answer

Expert verified

The solution for the system of linear equation is -2,0.

Step by step solution

01

Step 1. Given information.

Consider the given system of equations,

2x+y=-4x-y=-2

02

Step 2. Write in augmented form.

The augmented matrix for the given system of equations is

21-41-1-2

03

Step 3. Apply row operations.

Apply R12鈫�R1,

112-21-1-2

Apply R2-R1鈫�R2,

112-20-320

Apply -23脳R2鈫�R2,

112-2010

Now, the matrix is in row-echelon form.

04

Step 4. Write in system of equations.

Writing the corresponding system of equations,

x+12y=-2......(i)y=0......(ii)

Substitute yin equation (i),

x+12脳0=-2x=-2

05

Step 5. Check the answers.

Substitute the values x,yin equation (i),

-2+120=-2-2+0=-2-2=-2

This is true.

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