Question

Determine which if any of given ordered pairs satisfy the system of linear equations

Answer 1

Solution:

The equations are given below as

$\begin{gathered} x+3y-z=-11-----(1) \\ 2x-y+2z=11------(2) \\ 3x+2y+3z=6------(3) \end{gathered}$

Step 1:

Make x the subject of the formula from equation (1)

$\begin{gathered} x+3y-z=-11 \\ x=-11-3y+z-----(4) \end{gathered}$

Step 2:

Substitute equation (4) in equations (2) and (3)

$\begin{gathered} 2x-y+2z=11 \\ 2(-11-3y+z)-y+2z=11 \\ -22-6y+2z-y+2z=11 \\ -7y+4z=11+22 \\ -7y+4z=33-----(5) \\ \\ 3x+2y+3z=6 \\ 3(-11-3y+z)+2y+3z=6 \\ -33-9y+3z+2y+3z=6 \\ -7y+6z=6+33 \\ -7y+6z=39------(6) \end{gathered}$

Step 3:

Substract equation 5 from 6

$\begin{gathered} -7y-(-7y)+4z-6z=33-39 \\ -2z=-6 \\ z=3 \end{gathered}$

Step 4:

Substitute the value of z=3 in equation (4)

$\begin{gathered} -7y+4z=33 \\ -7y+4(3)=33 \\ -7y+12=33 \\ -7y=33-12 \\ -7y=21 \\ y=-3 \end{gathered}$

Step 4:

Substitute y=-3, z= 3 in equation (4)

$\begin{gathered} \begin{equation*} x=-11-3y+z \end{equation*} \\ x=-11-3(-3)+3 \\ x=-11+9+3 \\ x=1 \end{gathered}$

Hence,

The final answer is

$\Rightarrow(1,-3,3)$

ONLY THE ORDERED PAIR ( 1, -3, 3) satisfies the system of linear equations

OPTION B is the right answer