Question

how to solve the following system equation x+y-z=0 ,2x-3y+z=0 ,x-4y+2z=0​

Answer 1

Answer:

solve it by elimination method

Answer 2

From the first equation, we know that $z=x+y$.

Substitute $z=x+y$ into two equations.

$2x-3y+x+y=0$

∴ $3x-2y=0$

$x-4y+2x+2y=0$

∴ $3x-2y=0$

Then, solve the system equation above.

The two equation above has infinitely many solutions.

∴ The system equation has infinite solutions.