Solve Using a Matrix by Elimination -a+5b=12 , -a-3b=10

Problem

{[−a+5*b=12],[−a−3*b=10])

Solution

1. Write the augmented matrix representing the system of linear equations.

[[−1,5,|,12],[−1,−3,|,10]]

2. Create a leading 1 in the first row by multiplying the first row ((R_1) by −1

[[1,−5,|,−12],[−1,−3,|,10]]

3. Eliminate the first entry in the second row by adding the first row to the second row ((R_2)+(R_1)⇒(R_2).

[[1,−5,|,−12],[0,−8,|,−2]]

4. Create a leading 1 in the second row by dividing the second row by −8

[[1,−5,|,−12],[0,1,|,1/4]]

5. Eliminate the entry above the leading 1 in the second column by adding 5 times the second row to the first row ((R_1)+5*(R_2)⇒(R_1).

[[1,0,|,−12+5/4]]

[[1,0,|,−43/4],[0,1,|,1/4]]

6. Identify the values for the variables a and b from the resulting identity matrix.

a=−43/4

b=1/4

Final Answer

(a,b)=(−43/4,1/4)

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