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Row equivalent matrix method
4x-3y=11
3x+7y=-1​

User Tmandry
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1 Answer

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To solve the system of linear equations using the row echelon method, we start by writing the augmented matrix:

[4 -3 11 | 0]
[3 7 -1 | 0]

We want to eliminate the x-coefficient in the second row. To do this, we subtract 3/4 times the first row from the second row:

[4 -3 11 | 0]
[0 25/4 -25/4 | 0]

Next, we want to eliminate the y-coefficient in the first row. To do this, we add 3/4 times the second row to the first row:

[4 0 1 | 0]
[0 25/4 -25/4 | 0]

Now we have a triangular matrix, which we can solve by back substitution. From the second row, we get:

25/4*y = 25/4

y = 1

Substituting y = 1 into the first row, we get:

4x = -1

x = -1/4

Therefore, the solution to the system of linear equations is:

x = -1/4, y = 1.
User Scoutman
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