`8x - 4y = 7, 5x + 2y = 1` Use matricies to solve the system of equations (if possible). Use Gauss-Jordan elimination.

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Given system of equations are

`8x - 4y = 7, 5x + 2y = 1`

so the matrices A and B are given as follows

A = `[[8, -4], [5, 2]]`

B = `[[7], [1]]`

so the augmented matrix is [AB] = `[[8, -4, 7], [5, 2, 1]]`

on solving this we get the values of x,y .

step 1 .  Make the pivot in the 1st column by dividing the 1st row by 8

`[[1, -1/2, 7/8], [5, 2, 1]]`

                                 

step 2 . muptiply the 1st row by 5

`[[5, -5/2, 35/8], [5, 2, 1]]`

                                 

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

`[[1, -1/2, 7/8], [0, 9/2, -27/8]]`

                               

step 4 divide the second row by 9/2

`[[1, -1/2, 7/8], [0, 1, -3/4]]`

                                   

step 5 multiply the 2nd row by -1/2  and subtract the 2nd row from the 1st row

 `[[1, 0, 1/2], [0, 1, -3/4]]`

 

so, the values of x, y are x= 1/2 and y = -3/4

             

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