Hi I would like to know how to solve the linear system equation x+2y+z=a2?

Question

Hi I would like to know how to solve the linear system equation x+2y+z=a2 , x+ y + 3z=a ,3x+ 4y +7y =10 how to solve this type of Equation

Answer 1

Use Gaussian reduction and back-substitution, just like rou would any other linear system. But your results for x, y, and z will be 'parameterized' in terms of a. That is, each of them will be some linear function of a.

Doug

Answer 2

You have to discuss this if it's necessary.

x+2y+z = a^2
-x-y-3z = -a
_________
y - 2z = a^2 - a


-3x-3 y -9z=-3a
3x+ 4y +7y =10
___________
y-2z = 10-3a

In both cases you got y-2z. So, this will make some sense if a^2 - a= 10-3a. Otherwise, the system will be incompatible

If a^2 + 2a - 10 = 0 (you have to find a so that the system is compatible), then you have an infinit solution set

Write to me if you have more doubts

Ilusion