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

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

x=
y=

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

 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