Question

Which classification describes the following system of equations x=5 y=6 -x-y+z=0

Answer 1

The classification of the system of equations can be found to be c. The system of equations is independent and consistent.

What does the equation show ?

To determine whether the system is independent and consistent, substitute the values of x and y from the first two equations into the third equation:

-5 - 6 + z = 0

Simplifying this equation:

-11 + z = 0

Now, add 11 to both sides to isolate z:

z = 11

So, there is a unique solution for z that satisfies all three equations. The system is consistent because it has a solution, and it's independent because all three equations provide distinct information and are not redundant.

The options for this question are:

a. The system of equations is inconsistent.

b. The system of equations is dependent.

c. The system of equations is independent and consistent.

d. The system of equations is overdefined.

Answer 2

Those system of equations are called the system of linear equations with multiple variables.

Explanation:

Here it is given a system equations as

x = 5 ....... (1)

y = 6 ........... (2) and

- x - y + z = 0 ........ (3)

Those systems of equations are called the system of linear equations with multiple variables.

Those are linear equations as the maximum power of the variables is 1.

We can solve those equations with simple algebra.

Here, x = 5, y = 6 and z = x + y = 5 + 6 = 11 (Answer)