Solve the following simultaneous expression:
$x + y = 4;2x - 5y = 1$

Hint: According to the question we have to solve all the sets of simultaneous expression. So, in the first expression (i) $x + y = 4;2x - 5y = 1$ we have to multiply with 2 in the expression $x + y = 4$ to obtain the values of x and y now, we have to subtract both of the expressions obtained the value of x or y and after that we have to substitute the value of the variable obtained in the another expression to obtain the other variable.

Complete step-by-step solution:
Step 1: First of all we will solve the expression (i) $x + y = 4;2x - 5y = 1$ to find the values of x and y
Hence,
$
   \Rightarrow x + y = 4.............(a) \\
   \Rightarrow 2x - 5y = 1..........(b)
 $
On multiplying with 2 in the expression (a),
$
   \Rightarrow 2(x + y = 4) \\
   \Rightarrow 2x + 2y = 8.............(c)
 $
Now, to find the values of x and y we have to subtract (b) and (c) hence,
\[
   \Rightarrow (2x + 2y) - (2x - 5y) = 8 - 1 \\
   \Rightarrow 2x + 2y - 2x + 5y = 7 \\
   \Rightarrow 7y = 7 \\
   \Rightarrow y = 1
 \]
Now, to find the value of y we have to substitute the value of y in the expression (a),
$
   \Rightarrow (x + 7) = 4 \\
   \Rightarrow x = 4 - 7 \\
   \Rightarrow x = - 3
 $

The value of x is -3 and y is 1.

Note: To eliminate the terms of the given expressions it is necessary to make the terms or variables equal to the other term or variable to eliminate them.
If one if the variable or root is obtained we can also obtain the other variable by substituting the value into any one of the given expressions/equations.