Question

Are there no solutions, many solutions or one solution to the following system of equations? X+3y +2z= 2 -2x-2y=-12 and -x-2y -z =-4?

Answer 1

The system of equations written in row form is;

`\begin{bmatrix}{1} & {3} & {2} & {2} \\ {-2} & {-2} & {0} & {-12} \\ {-1} & {-2} & {-1} & {-4} \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}}\end{bmatrix}`

The reduced row echelon form is;

`\begin{bmatrix}{1} & {0} & {-1} & {8} \\ {0} & {1} & {1} & {-2} \\ {0} & {0} & {0} & {0} \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}}\end{bmatrix}`

This shows that the equation has infinitely many solutions.