# Find all solutions of the following systems using Gaussian elimination. x + 2y + 3z = 4 2x + 5y...

## Question:

Find all solutions of the following systems using Gaussian elimination.

x + 2y + 3z = 4

2x + 5y + 7z = 10

2y + 2z = 4

## Gauss Elimination

Gauss elimination is a technique to solve a system of linear equations by eliminating the unknowns from the equations in such a manner that the matrix of the system is a upper triangular matrix.

To solve a system that is upper triangular, we just backsubstitute the variables in the upper equations, starting with the lowest equation.

To apply Gauss elimination, we will do row operations on the matrix of the system.

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To solve the system {eq}\displaystyle \begin{align} \begin{cases} x + 2y + 3z = 4\\ 2x + 5y + 7z = 10\\ 2y + 2z =...