Question

Make up a system of three linear equations containing three variables that has: (a) No solution (b) Exactly one solution (c) Infinitely many solutions Give the three systems to a friend to solve and critique.

Short answer

a)The system of the equation having no solution is :

$\left\{\begin{array}{ll}2x+4y+6z=& 1\\ 4x+8y+12z=& 2\\ 6x+12y+18z=& 3\end{array}\right.$

Step-by-step solution

Step 1. Given information:

We have to make three different systems of the equation of 3 variables having no solution, unique solution, and infinite solutions.

Step 2. To make system of equations:

System: