Find Reduced Row Echelon Form [[(x-3y)=10],[(4x+3y)=10]]

Problem

{[x−3*y=10],[4*x+3*y=10])

Solution

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

[[1,−3,10],[4,3,10]]

2. Eliminate the x term from the second row by replacing (R_2) with (R_2)−4*(R_1)

[[1,−3,10],[0,15,−30]]

3. Normalize the second row by dividing (R_2) by 15

[[1,−3,10],[0,1,−2]]

4. Eliminate the y term from the first row by replacing (R_1) with (R_1)+3*(R_2)

[[1,0,4],[0,1,−2]]

Final Answer

RREF*[[1,−3,10],[4,3,10]]=[[1,0,4],[0,1,−2]]

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