Solve Using a Matrix by Elimination a+2b=4 , -2a+4b=-8

Problem

{[a+2*b=4],[−2*a+4*b=−8])

Solution

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

[[1,2,|,4],[−2,4,|,−8]]

2. Eliminate the variable a from the second row by adding 2 times the first row to the second row ((R_2)←(R_2)+2*(R_1).

[[1,2,|,4],[0,8,|,0]]

3. Solve for b by dividing the second row by 8 ((R_2)←1/8*(R_2).

[[1,2,|,4],[0,1,|,0]]

⇒b=0

4. Back-substitute the value of b into the first row equation to solve for a ((R_1)←(R_1)−2*(R_2).

[[1,0,|,4],[0,1,|,0]]

⇒a=4

Final Answer

(a,b)=(4,0)

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