Question

How do you solve using gaussian elimination or gauss-jordan elimination, `2x + 3y = -2`, `-6x + y = -14`?

Answer 1

`color(brown)(((1,0,|,+2),(0,1,|,-2)))`

`x=2 and y=-2`

Explanation:

Using the form:

`(x,y,|,"answer")`

`color(brown)(((2,3,|,-2),(-6,+1,|,-14)))`
`" "(-3)xxRow_1`
`" "darr`

`color(brown)(((-6,-9,|,+6),(-6,+1,|,-14)))`
`" "Row_1-Row_2`
`" "darr`

`color(brown)(((0,-10,|,+20),(-6,+1,|,-14)))`
`" "Row_1-:(-10)`
`" "darr`

`color(brown)(((0,+1,|,-2),(-6,+1,|,-14)))`
`" "Row_2-Row_1`
`" "darr`

`color(brown)(((0,+1,|,-2),(-6,0,|,-12)))`
`" "Row_2-:(-6)`
`" "darr`

`color(brown)(((0,+1,|,-2),(+1,0,|,+2)))`

Write in row echelon form

`color(brown)(((1,0,|,+2),(0,1,|,-2)))`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check that `x=2 and y=-2`

`2x+3y=-2" "->" "LHS->2(2)+3(-2)=4-6=-2`

`-6x+y=-14" "->" "LHS->-6(2)+(-2)=-14`