Given Equations:
The given equations are:
1. x + y = 4
2. 2x - 5y = 1

Solving the Equations:
To solve the given equations, we can use the method of substitution or elimination.

Method 1: Substitution
In this method, we solve one equation for one variable and substitute it into the other equation.

Step 1: Solve the first equation for x
From the first equation, we have:
x = 4 - y

Step 2: Substitute the value of x into the second equation
Substituting x = 4 - y in the second equation, we get:
2(4 - y) - 5y = 1
8 - 2y - 5y = 1
8 - 7y = 1
-7y = 1 - 8
-7y = -7
y = -7 / -7
y = 1

Step 3: Substitute the value of y into the first equation to find x
Using y = 1 in the first equation, we have:
x + 1 = 4
x = 4 - 1
x = 3

Therefore, the solution to the given equations is x = 3 and y = 1.

Method 2: Elimination
In this method, we eliminate one variable by adding or subtracting the equations.

Step 1: Multiply the first equation by 2
By multiplying the first equation by 2, we get:
2x + 2y = 8

Step 2: Subtract the second equation from the modified first equation
Subtracting the second equation from the modified first equation, we have:
(2x + 2y) - (2x - 5y) = 8 - 1
2x + 2y - 2x + 5y = 7
7y = 7
y = 7 / 7
y = 1

Step 3: Substitute the value of y into the first equation to find x
Using y = 1 in the first equation, we have:
x + 1 = 4
x = 4 - 1
x = 3

Therefore, the solution to the given equations is x = 3 and y = 1.

Summary:
The given equations x + y = 4 and 2x - 5y = 1 can be solved using the substitution method or elimination method. By solving the equations using either method, we find that the solution is x = 3 and y = 1.