# System of equations with insufficient equations [closed]

I have a system of equations problem with $5$ variables but only $4$ equations:

Suppose that $x,y,z,u$ and $v$ are real numbers that satisfy the following system: \begin{align} -4x + 6y + 14z + 4v &= -8\\ -3x + 9y + 15z - u + 3v &= 6\\ -3x + 6z + u + 3v &= -18\\ -x + 2y + 4z + v &= -1\\ \end{align} Which of the following statements are true?

i. $y + z = 2$

ii. $v = 0$

iii. $x - 2z - v = 5$

iv. $y + z - u = 5$

Ans: The correct statements are: __

A. i. and iii.

B. i., ii., and iii.

C. i., iii., and iv.

D. i. and ii.

E. All

How should I approach the problem considering there are more variables than equations?

## closed as off-topic by Did, Andrew D. Hwang, user63181, user91500, azimutApr 13 '14 at 14:41

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Andrew D. Hwang, Community, user91500, azimut
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• Irrespective of numbers of variables and equations, a way to approach such problems is to set up the augmented matrix representing the system of equations and then use elementary row operations to bring it to reduced row-echelon form; from there it will probably be easy to see what the answer is. – Gerry Myerson Apr 13 '14 at 11:17