Question

solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations. x-2y+3z=-2. 6x+2y+2z=-48. x+4y+3z=-38​

Answer 1

C. -5, -6, -3

to my EDG peeps :)

Answer 2

x = -5, y = -6, z = -3

Explanation:

Given the system of three equations:

`\left\{\begin{array}{l}x-2y+3z=-2\\6x+2y+2z=-48\\x+4y+3z=-38\end{array}\right.`

Write the augmented matrix for the system of equations

`\left(\begin{array}{ccccc}1&-2&3&|&-2\\6&2&2&|&-48\\1&4&3&|&-38\end{array}\right)`

Find the reduced row-echelon form of the augmented matrix for the system of equations:

Thus, the system of three equations is

`\left\{\begin{array}{r}x+3z-2y=-2\\16z-14y=36\\-6y=36\end{array}\right.`

From the last equation:

`y=-6`

Substitute it into the second equation:

`16z-14\cdot (-6)=36\\ \\16z=36-84\\ \\16z=-48\\ \\z=-3`

Substitute y = -6 and z = -3 into the first equation:

`x+3\cdot (-3)-2\cdot (-6)=-2\\ \\x=-2+9-12\\ \\x=-5`