Solve x + y + z = 122x – y – z = -6x + 3y + 5z = 44

Question

i need solved

Solve x + y + z = 122x – y – z = -6x + 3y + 5z = 44

Answer 1

System of 3 linear equations in 3 unknowns:

x + y + z = 122

x – y – z = -6

x + 3y + 5z = 44

 

There are many methods. One is using the Calculator(e.g. TI-84) has a lovely rref function that operates on the augmented 3 by 4 matrix.

 

Using determinants (Cramer's Rule) is also available.*

 

Manual methods with paper & pencil, involving row operations, are taught in Algebra II classes--but human nature being what it is, they can be somewhat error prone.  Any time you develop a set of answers for (x,y,z) using manual methods, you MUST check those answers in all 3 equations to be sure that no error has crept in.

 

* I recommend this method.  If the System Determinant value is 0, then either the system has no solution or it's dependent. You can evaluate determinants either manually or by use of calculator.

 

You would not be having this kind of problem for homework unless your course instructor had covered some method for doing it.  You have to do the work yourself in order to benefit and become prepared to pass tests.  Again, remember to check your answers.