Question

Which classification describes the following system of equations? inconsistent and dependent consistent and dependent consistent and independent inconsistent and independent.

Answer 1

The system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have three linear equations in three variables:

x - y - z = 0 ..(1)

2x - y + 2z = 1 ..(2)

x - y + z = -2 ..(3)

From the equation (1):

$\rm x=y+z$

Plug this value in the equation (2) and (3):

$\rm 2\left(y+z\right)-y+2z=1\\\\ y+z-y+z=-2$

After solving we get:

z = -1

y = 5

Plug the above two values in equation (1) we get:

x = 4

Thus, the system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

Learn more about the linear equation here:

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