Find Reduced Row Echelon Form [[-10x-y=3],[-8x+y=15]]

Problem

{[−10*x−y=3],[−8*x+y=15])

Solution

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

[[−10,−1,|,3],[−8,1,|,15]]

2. Add the first row to the second row to eliminate the y coefficient in the second row.

(R_2)→(R_2)+(R_1)

[[−10,−1,|,3],[−18,0,|,18]]

3. Divide the second row by −18 to solve for x

(R_2)→(R_2)/(−18)

[[−10,−1,|,3],[1,0,|,−1]]

4. Swap the first and second rows to place the leading one in the first column.

(R_1)↔(R_2)

[[1,0,|,−1],[−10,−1,|,3]]

5. Eliminate the x term in the second row by adding 10 times the first row to the second row.

(R_2)→(R_2)+10*(R_1)

[[1,0,|,−1],[0,−1,|,−7]]

6. Multiply the second row by −1 to solve for y

(R_2)→−1⋅(R_2)

[[1,0,|,−1],[0,1,|,7]]

Final Answer

[[1,0,|,−1],[0,1,|,7]]

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