Question

How do you solve `2x + 6y = 2` and `x + 5y = 3` using matrices?

Answer 1

`(x,y)=(-2,1)`
(see below for solution using matrices).

Explanation:

Write the given equations
`color(white)("XXX")2x+6y=2`
`color(white)("XXX")x+5y=3`
in augmented matrix form
`color(white)("XXX")( (2,6,2),(1,5,3))`

Divide the first row by `2`
`color(white)("XXX")((1,3,1),(1,5,3))`

Subtract the (new) first row from the second row
`color(white)("XXX")((1,3,1),(0,2,2))`

Divide the (new) second row by `2`
`color(white)("XXX")((1,3,1),(0,1,1))`

Subtract `3` times this second row from this first row
`color(white)("XXX")((1,0,-2),(0,1,1))`

Note that this is equivalent to the expressions
#color(white)("XXX"){: {:(1x,+0y,=-2),(0x,+1y,=1):}} rArr {:(x=-2),(y=1):}#