I'd like to give you a solution while pointing out something to look for in the future. We have the system
x + y = 2 2x - y = -1
Let me move the y in the second equation over to the right and the -1 to the left.
x + y = 2 2x + 1 = y
Now, I'll use the symmetric property on the second equation, which tells me that I can flip the equation without changing it.
x + y = 2 y = 2x + 1
Now, in the first equation, move the x to the right by subtracting it from both sides.
y = 2 - x y = 2x + 1
Now, each equation represents a line and you're trying to figure out if they intersect. I'll assume that they do intersect. If they don't intersect, I'll get some nonsense like 0 = 2 because its a bad assumption. If they do, I'll get the solution. And if
I look at my equations, each has a y on the left. So, I can equate them.
2 - x = 2x + 1
Add x to both sides
2 = 3x + 1
Subtract 1 from both sides
1 = 3x
Divide both sides by 3.
x = 1/3
Plug this guy into one of the equations to get y = 5/3.
What I want to point out is that if you look at the original equations, the numbers in front of the y's differ only by a sign, which you can change by moving one to the other side. If the y's are on one side of the equation and they have the same number
and sign in front, then you can equate them! This would work even if each equation had 5.3y instead of y because of the substitution property.
Hope this helps.