Thread: Use the echelon method to solve the following system of two equations in two unknowns

x+y=6
4x-y=19

Thank you

Originally Posted by Niaboc

x+y=6
4x-y=19

Thank you

You need to put it in matrix form, then row reduce.

So, start with:
[1 1 6
4 -1 19]

Add row 1 to row 2:
[1 1 6
5 0 15]

Divide row 2 by 5:
[1 1 6
1 0 3]

Swap rows:
[1 0 5
1 1 6]

At this point, you have echelon form. The easiest way to go from here is to note x = 5, and substitute into y + x = 6.
However, if you need to be in reduced echelon form:
Subtract row 1 from row 2:
[1 0 5
0 1 1]

This gives you the two solution equations:
x = 5
y = 1

Hope this helps.