Question

Find the system of linear equations represented by the augmented matrix. Then use back substitution to solve. (Use variables x, y, z, and w if applicable.)
[ 1 2 -2 : 3
0 1 1 : -15
0 0 1 : -5 ]
(x, y, z) = ______.

Answer 1

Answer:

x = 13       y  =  - 10     z  =  -5

Step-by-step explanation:

In the augmented matrix of a system of linear equation, each row represent an equation, and each column represent variables and constants

Therefore the linear equation for the augmented matrix

1  2  -2  : 3  

0  1   1  : -15

0  0   1 : -5

Is in terms of  x  y  z  and  w, the equation system:

1*x  +  2*y  - 2*z  =  3

0*x +  1* y   +  1*z   = -15

0*x  + 0*y + 1*z = -5

To solve it we proceed as follows

from the last equation      z  =  -  5

plugging this value in the second equation

y  +  z  =  - 15

y   -  5 =  - 15

y  =  - 10

And finally

x  + (2)*(-10) - 2*( - 5 )  =  3

x  -  20  + 10  = 3

x  -  10  = 3

x  =  13