This is called system of equations because you are searching a pair of numbers that inserted as x and y verify both equations at the same time.
To solve a system of equation you have to use one equation to express one variable as a function of the other, and substitute the result in the second equation.
In your case you have
y = x - 2
So your y variable will be always equal to x - 2 , even in the second equation. Then we can write
x - 2 = 4x + 1
Here I replaced the "value" of y in the second equation.
Now you have an equation in one variable that you can solve as usual
x - 2 = 4x + 1
4x - x = - 2 - 1
3x = -3
x = -1
With a value for x you can substitute in one of the two equations and obtain y. Because both equations has to be valid at the same time, both equations must give you the same number for y. Let's try:
y = x - 2
y = - 1 - 2
y = -3
and, with the second equation
y = 4x + 1
y = 4 ( - 1 ) + 1
y = - 4 + 1
y = -3
It works! Then our solution is given by x = -1 and y = -3.
To graph this, simply plot these coordinates.