Question

Solve the system ⎧⎩⎨⎪⎪⎪⎪⎪⎪4x1−x13x1−3x1−5x2+x2−4x2+3x2+4x3+2x3+6x3+6x3+4x4=+3x4=+7x4=+9x4=3143

Answer 1

It appears you have the system with augmented matrxi ...

$\left[\begin{array}{cccc|c}4&-5&4&4&3\\-1&1&2&3&1\\3&-4&6&7&4\\-3&3&6&9&3\end{array}\right]$

Right away, you notice that the 4th row is 3 times the 2nd row, so the equations are dependent and will not have a unique solution.

My calculator tells me the reduced equations can be written

... x1 -14x3 -19x4 = -8

... x2 -12x3 -16x4 = -7

This says there are two dependent equations in the set, not just one.