can i please actually receive help because i need it please please please someone

Question

Classify the system and identify the number of solutions.

x − 2y + z = −7

x − 5y − z = −5

x − 8y − 3z = −3

A.) consistent, independent; one

B.) inconsistent; none

C.) consistent, dependent; none

D.) consistent; dependent; infinite

Please give and only give the explanation and solution.

Answer 1

Ok I want you READ THROUGH the problem solution.

The next problem I want you to take what you have

learned and APPLY it to the new problem.

Dependent means one of the equations is REDUNDANT..

It is a combination of the other equations, causing it

to completely drop out. As a result you will have

FEWER equations than variables, which means the system

has infinitely many solutions.

Inconsistent means that two equations have the same

left side, but the RIGHT sides are DIFFERENT, which is

not allowed. The system then has NO SOLUTION

Step 1: Look down the COLUMNS and choose the variable that

is the "LIGHTEST".... small or no coefficients,

and positive... the smaller and more positives the better...

Column X is the lightest, becuase all of the coefficients are ONE (1)

(because there are no coefficients of x, so they are understood to be 1)

X is the best variable to eliminate

STep 2: PAIRS UP EQUATIONS 1 and EQUATION 2, and then ELIMINATES the

chosen variable

This can be done simply by subtracting the equations...

x - x - 2y - -5y + z - -z = -7 - -5

-2y + 5y + z + z = -7 + 5

3y + 2z = -2

Step 3: PAIRS UP EQUATIONS 2 and EQUATION 3, and then ELIMINATES the

SAME variable !!! You MUST ELIMINATE THE SAME VARIABLE you chose

in the first 2 steps

this can be done again by subtracting the equations...

x - x - 5y - -8y -z - -3z = -5 - -3

-5y + 8y - z + 3z = -5 + 3

3y + 2z = -2

Notice the equations are the same, so we're going to try one last step..

EQUATION 1 vs EQUATION 3: Also done by subtracting them

x - x - 2y - - 8y +z - -3z = -7 - -3

-2y + 8y + z + 3z = -7 + 3

6y + 4z = -4

3y + 2z = -2 <-- divides by 2 and it's STILL the same!!!

So we have one equation and 3 unknowns

The system is dependant, consistent, and has infinite number of solutions

The only other thing that SHOULD be done is to choose a FREE variable, say z,

and write x and y in terms of z.

option D is the answer