I totally get it. Elimination confused the heck out of me at first. I'll do number 1 both ways and let you take the rest.
x + 4y = -4
x + 10y = -16
We can solve both for x. Then, since x equals two different things, they must equal each other!
x = -4y - 4
x = -10y - 16
-4y - 4 = -10y - 16
6y = -12
y = -2
x = -4(-2) - 4
x = 8 - 4
x = 4
Let's check.
4 + 10(-2) = -16
4 - 20 = -16
-16 = -16
0 = 0
4 + 4(-2) = -4
4 - 8 = -4
-4 = -4
0 = 0
Check. Our answer is (4, -2).
We can also solve one equation for x and substitute.
x = -4y - 4
-4y - 4 + 10y = -16
6y = -12
y = -2
x = -4(-2) - 4
x = 8 - 4
x = 4
(4, -2)
OK, let's do substitution. We need either the x's or the y's to be opposites so they add to 0 and cancel out. Multiplying an equation by any factor still gives us the same graph.
Now, it's obvious to me that we could multiply either the top or bottom by -1 to get x and -x.
-x - 4y = 4
x + 10y = -16
Adding the equations together...
6y = -12
y = -2
Etc...
Or...
x + 4y = -4
-x - 10y = 16
-6y = 12
y = -2
Etc...
We could even do the y's. The LCM of 4 and 10 is 20, so what if we multiply the top by 5 and the bottom by -2 (or -5 and 2).
5x + 20y = -20
-2x - 20y = 32
3x = 12
x = 4
Etc...
Or...
-5x - 20y = 20
2x + 20y = -32
-3x = -12
x = 4
Etc...
I hope this gives you a good base. Go!
