`5x - 5y = -5, -2x - 3y = 7` Use matricies to solve the system of equations (if possible). Use Gauss-Jordan elimination.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Given system of equations are

5x - 5y = -5, -2x - 3y = 7

so ,we get the matrices as

A = `[[5, -5], [-2, -3]]`

and

B = `[[-5], [7]]`

the augmented matrix [AB] = `[[5, -5, -5], [-2, -3, 7]]`

 

 

on solving the [AB] we get the values of x,y

Step 1. Make the pivot in the 1st column by dividing the 1st row by 5

`[[1, -1, -1], [-2, -3, 7]]`

 

step 2. Multiply the 1st row by -2

`[[-2, 2, 2], [-2, -3, 7]]`

 

step 3. Subtract the 1st row from the 2nd row

`[[1, -1, -1], [0, -5, 5]]`

 

step 4. divide the second row with -5 we get

`[[1, -1, -1], [0, -1, 1]]`

 

Step 5.  subtract the 2 nd row from 1st row we get

`[[1, 0, -2], [0, -1, 1]]`

                 

step 6. multiply the 2 nd row with -1

`[[1, 0, -2], [0, 1, -1]]`

 

 

so the vlaues of x,y are x= -2 , y =-1

 

Approved by eNotes Editorial Team