How do you solve the following system $ - 2x + y = 5,4x - 2y = 9 $ ?

Hint: In order to determine the solution, rewrite the second equation by dividing both sides of the equation with the number $ - 2 $ . We will clearly know that the system of equations is actually the same as they are of the form $ - 2x + y = \lambda $ . So for such a system of equations, no solution exists.

Complete step by step solution:
We are given pair of linear equation in two variables $ - 2x + y = 5,4x - 2y = 9 $
 $ - 2x + y = 5 $ ---(1)
 $ 4x - 2y = 9 $
Rewriting the equation by dividing both sides of the equation with $ - 2 $
\[\Rightarrow \dfrac{1}{{ - 2}}\left( {4x - 2y} \right) = \dfrac{9}{{ - 2}}\]
\[\Rightarrow - 2x + y = - \dfrac{9}{2}\]----(2)
If we look at both the equations carefully, both the equations (1) and (2)are actually same as they have the form $ - 2x + y = \lambda $
Since the system of equations are identical so no solution exists for such a system.
Therefore, the answer is that no solution exists for the given system of equations.

Note: Linear Equation in two variable: A linear equation is a equation which can be represented in the form of $ ax + by + c $ where $ x $ and $ y $ are the unknown variables and c is the number known where $ a \ne 0,b \ne 0 $ .
The degree of the variable in the linear equation is of the order 1.
1. One must be careful while calculating the answer as calculation error may come.