# How do you solve using gaussian elimination or gauss-jordan elimination, #3x + y =1 #, #-7x - 2y = -1#?

##### 1 Answer

This can be rewritten into an **augmented matrix** form:

#[(3,1,|,1),(-7,-2,|,-1)]# where each entry is a coefficient associated with each variable, and the last column contains the answers to each equality.

To get this into **row echelon** form, we need to get leading

To get it into **reduced-row echelon** form, get all numbers above AND below each leading

*I am using the notation where the rightmost indicated row is the one that is operated upon.*

#stackrel(3R_1 + R_2" ")(->)[(3,1,|,1),(2,1,|,2)]#

#stackrel(-R_2 + R_1" ")(->)[(1,0,|,-1),(2,1,|,2)]#

#stackrel(-2R_1 + R_2" ")(->)[(color(blue)(1),0,|,color(blue)(-1)),(0,color(blue)(1),|,color(blue)(4))]#

From here we can just bring it back to algebraic form to get:

#color(blue)(x = -1)#

#color(blue)(y = 4)#

We can check to see that this is correct by plugging these back in:

#3(-1) + (4) = -3 + 4 = 1#

#-7(-1) - 2(4) = 7 - 8 = -1#