Question 540958
Too many minus signs, probably. Those minus signs can get you. They got me once (very embarrassing). It's also an ugly system for elimination; substitution looks more appealing.
I would multiply by -3 {{{-2x - 8y = 22}}} to get
{{{6x +24y = -66}}} and I would add that to
{{{-6x - y = 20}}} to get
{{{23y=-46}}} --> {{{y=-2}}}
Then substituting that in {{{-6x - y = 20}}} I would get
{{{-6x -(-2) = 20}}} --> {{{-6x +2 = 20}}}
Then subtracting 2 from both sides I would get
{{{-6x=18}}} ---> {{{x=18/(-2)=-9}}}
So the solution is x=-9 , y=-2, or (-9, -2).
Here's my philosophy about minus signs:
A minus sign is part of the number that follows (if there is a number after the minus sign).
If you see a minus sign in front of something that is not a number, that something is really multiplied by (-1).
So, I see the equation {{{(-6)x + (-1)y = 20}}} where {{{-6x - y = 20}}} is written.
There is no such thing as subtraction, it's just adding a negative number. (There's no division either, you just multiply by the reciprocal, the upside-down fraction).
I do not think I've convinced many that subtraction (and division) do not really exist (a point of view I learned in college). The idea is too ingrained. The problem is that teachers teach subtraction in first grade and continue preaching it throughout your schooling. If they introduced negative numbers in first grade, they would not need to introduce that s-word, and student's troubles with algebra would be a lot less serious.