Question

Solve the given system of equations by either Gaussian elimination or Gauss-Jordan elimination. (If the system is inconsistent, enter INCONSISTENT. If the system is dependent, express x, y, and z in terms of the parameter t.) 5x − 2y + 4z = 12 x + y + z = 8 4x − 3y + 3z = 4 (x, y, z) = 2(−3z+14) 7​, −z+28 7​,t

Answer 1

Required unique solutions are 8, 4, 0 and the system is consistant.

Explanation:

Given system of equation,

5x-2y+4z=12

x+y+z=8

4x-3y+3z=4

To find solution of the system re-write as,

`\left[\begin{array}{ccc}5&-2&4 :12\\1&1&1 : 8\\4&-3&3 : 4\end{array}\right]\to\left[\begin{array}{ccc}1&1&1 :8\\5&-2&4 : 12\\4&-3&3 : 4\end{array}\right] (R_1\iff R_2)\\\implies \left[\begin{array}{ccc}1&1& 1:8\\0&-7&-1 : -28\\0&-7&-1 : -28\end{array}\right] (R_(2)^(')=R_2-5R_1,R_(3)^(')=R_3-4R_1)\\\implies \left[\begin{array}{ccc}1&1&1 :8\\0&-7&-1 :-28\\0&0&0 : 0\end{array}\right] (R_(3)^(')=R_3+R_2)\\\implies \left[\begin{array}{ccc}1&1&1 :8\\0&1&1/7 : 4\\0&0&0 : 0\end{array}\right]`

Hence solutions are 8, 4 and 0. And it is a unique solution. Therefore system is consistent.