Question

How do you solve the system `-2x+3y=-9` and `-x+-3y=-3`?

Answer 1

Solve the two possibilities separately:
`{(-2x+3y=-9),(-x+3y=-3):} and {(-2x+3y=-9),(-x-3y=-3):}`
giving `(x,y)=(6,1)` and `(x,y)=(4,-1/3)`

Explanation:

Case 1:
`{([1]color(white)("XXX")-2x+3y=-9),([2]color(white)("XXX")-x+3y=-3):}`
subtracting [2] from [1]
`[3]color(white)("XXXX")` `-x =-6`
`[4]color(white)("XXXX")` `x=6`
substituting `x=6` in [2]
`[5]color(white)("XXXX")` `-6+3y = -3`
`[6]color(white)("XXXX")` `y=1`

Case 2:
`{([7]color(white)("XXX")-2x+3y=-9), ([8]color(white)("XXX")-x-3y=-3):}`

`[9]color(white)("XXXX")-3x = -12`
`[10]color(white)("XXXX")x==4`

`[11]color(white)("XXXX")-4-3y = -3`
`[12]color(white)("XXXX")y=-1/3`