Question

Check whether the following system of equations has a solution.
4x+2y+8z+6w=4
2x+2y+2z+2w=0
x+3z+2w==3

Answer 1

Note that 3 linear equations in 4 unknowns cannot result in a single solution. There will either be no solution or an infinite number of solutions.

Subtracting the second equation from the first, we get:

$2x+6z+4w=4; \\$

Dividing that by 2, we get:

$x+3z+2w=2; \\$

This contradicts to the formula of the third equation, so this system has no solution.

Source:

https://socratic.org/questions/check-whether-the-following-system-of-equations-has-a-solution-4x-2y-8z-6z-3-2x-