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System Matrix Help PLEASE!!!! - solve for two unknowns











































Solve the following system
x-8/2 + y+10/3 =4
x -2y =5

x=
y=

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Mar 25, 2011
System Matrix - solve for two unknowns
by: Staff


The question:

Solve the following system

x-8/2 + y+10/3 =4
x -2y =5

x=
y=

The answer:

The following two equations need to be in the standard format (Ax + By + Cz = D) before proceeding:

x - 8/2 + y +10/3 =4

x -2y =5


1st equation – put in standard format

x - 8/2 + y +10/3 = 4

x - 4 + y +10/3 = 4

x – 4 + 4 + y +10/3 = 4 + 4

x + 0 + y +10/3 = 8

x + y + 10/3 = 8

x + y + 10/3 - 10/3 = 8 - 10/3

x + y + 0 = 8 - 10/3

x + y = 8 - 10/3

x + y = 24/3 - 10/3

x + y = 14/3


2nd equation is already in the standard format

x - 2y =5


The two equations, in the standard format (Ax + By + Cz = D):

x + y = 14/3

x - 2y =5



Prepare an Augmented Matrix of 2 rows and 3 columns.

Each row in the Augmented Matrix will represent one of the two equations.

The first number in each row is the coefficient for the x variable, the second number in each row is the coefficient for the y variable, and the last number will be the constant:

|…………..…|
| 1 1 : 14/3….|
| 1 -2 : 5… . . .|
|………………|

x + y = 14/3

x - 2y =5

Convert the Augmented Matrix into a triangular form.

|…………..…|
| 1 1 : 14/3….|
| 1 -2 : 5… . . .|
|………………|

add -1 times the 1st row to the 2nd row


|…………..…|
| 1 1 : 14/3….|
| 1 -3 : 1/3… . . .|
|………………|

multiply the 2nd row by -1/3

|…………..…|
| 1 1 : 14/3….|
| 0 1 : -1/9… . . .|
|………………|

add -1 times the 2nd row to the 1st row

the matrix is now is reduced row echelon form

|…………..…|
| 1 0 : 43/9….|
| 0 1 : -1/9… . . .|
|………………|

Convert the matrix back to equation form:


The solution to the two simultaneous equations is:

From row 1, x = 43/9

From row 2, y = -1/9


The final answer to your question is:

x = 43/9

y = -1/9


Check the answer by substituting the numerical values of x and y into the original equations:

x + y = 14/3

43/9 + (-1/9) = 14/3, correct


x - 2y =5

43/9 - 2*(-1/9) = 5, correct


Since the numerical values of x and y work in both of the original equations, the solutions are correct.



Thanks for writing.


Staff
www.solving-math-problems.com



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