Question

Solve the following linear equations by Cramer’s Rule:

2x – y + z = 1, x + 2y + 3z = 8, 3x + y – 4z = 1

Answer 1

Given equations are 

2x – y + z = 1 

x + 2y + 3z = 8 

3x + y – 4z = 1

D=\(\begin{vmatrix}2&-1&1\\1&2&3\\3&1&-4\end{vmatrix}\)

= 2(-8 – 3) – (-1)(-4 – 9) + 1(1 – 6) 

= 2(-11) + 1(-13) + 1(-5) 

= -22 – 13 – 5 

= -40 ≠ 0

∴ x = 1, y = 2 and z = 1 are the solutions of the given equations.