Solve Using a Matrix by Elimination a+3b=1 , 3a-2b=14

Problem

{[a+3*b=1],[3*a−2*b=14])

Solution

1. Write the system of equations as an augmented matrix.

[[1,3,|,1],[3,−2,|,14]]

2. Eliminate the a term in the second row by replacing the second row ((R_2) with (R_2)−3*(R_1)

[[1,3,|,1],[0,−11,|,11]]

3. Scale the second row to solve for b by dividing (R_2) by −11

[[1,3,|,1],[0,1,|,−1]]

4. Eliminate the b term in the first row by replacing (R_1) with (R_1)−3*(R_2)

[[1,0,|,4],[0,1,|,−1]]

5. Identify the values of the variables from the resulting identity matrix.

a=4

b=−1

Final Answer

(a,b)=(4,−1)

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