Simultaneous Equation help please?

x - y = 2 (solve by using elimination)
2y = x + 1

2y = x + 1
x - 2y = -1

...x - y = 2
–) x - 2y = -1 (subtraction)
------------------------
y = 3

x - y = 2
x - 3 = 2
x = 2 + 3
x = 5

∴ x = 5 , y = 3

here's an alternative way;

put into matrix form

x-y 2
-x+2y 1

1 -1 2
-1 2 1

1 -1 2
0 1 3

1 0 5
0 1 3

x 0 5
0 y 3


solution set; [5,3]

x - y = 2
x - 2y = - 1

x - y = 2
- x + 2y = 1----------ADD

y = 3

x - 3 = 2
x = 5

x = 5 , y = 1

You need substitute for either x or y in to the formula.

As x-y=2

x=2 + y

Also 2y = x + 1

but you know that x = 2 +y
so
2y= x + 1
2y=(2 + y) +1
2y=3 + y
y=3

and as x-y=2
x=y+2
x=3+2
x=5

two equations:
1. x - y=2
2. 2y= x +1

from equation 1, x= 2 +y
then you substitute this value for x into equation 2

2y= 2 +y +1
so y = 3

then sub this y value back into equation 1

x= 2+3
so x= 5

therefore x= 5 and y= 3

and thats it!