Show that the system of equations shown below has infinitely many solutions

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Show that the system of equations shown below has infinitely many solutions, and find the general solution.

\begin{aligned}x + y - z &= 2 \quad [1] \\x - 2y + z &= 5 \quad [2] \\3x - 3y + z &= 12 \quad [3]\end{aligned}