Solve the following system of equations using matrices​ (row operations). x-y=3
6x-5z=36
6y+2z=18

(6,3,0)

Step-by-step explanation:

Given,

x -  y + 0z  =  3

6x -  0y - 2z = 36

0x + 6y + 2z = 18

You have the following augmented matrix:

(1) 1     -1     0      3

(2) 6    0   -2      36

(3) 0    6    2       18

Let's (3) add to (2) and divide by 6

(1)  1    -1    0       3

(2) 1     1    0       9

(3) 0    6   2       18

Now, let's (2) add  to (1) and divide by 2

(1)  1   0    0     6

(2) 1    1    0     9

(3) 0   6   2     18

Let's (3) ÷ 2

(1)  1    0   0     6

(2) 1    1   0      9

(3) 0   3   1      9  

Let's (1) subtract from (2)

(1)  1   0   0     6

(2) 0   1   0     3

(3) 0   3   1     9

Finally, let's (2) multiply by 3 and subtract from (3)

(1)  1   0   0     6

(2) 0   1   0     3

(3) 0   0   1     0

Thus,

x = 6, y = 3 and z = 0

The answer is (6, 3, 0)

We have to verify the answer

6 - 3 = 3  ⇒⇒ 3 = 3

6*6 - 5*0 = 36   ⇒⇒ 36 = 36

6*3 + 2*0 = 18    ⇒⇒ 18 = 18  

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step-by-step explanation: