Question

Check given point is the solutions of the equation \[x - 2y = 4\] or not: \[\left( {0,2} \right)\]

Answer 1

Hint: Here, we will first in a coordinate \[\left( {0,2} \right)\], where 0 is the value of \[x\] and 2 is the value of \[y\]. Then we will check if this point is a solution of the given equation, which is a value we can put in place of a variable that makes the equation true, that is, the left hand side is equal to the right hand side in the equation or not.

Complete step-by-step answer:
We are given that the equation is
\[x - 2y = 4{\text{ ......eq(1)}}\]
We know that in a coordinate \[\left( {0,2} \right)\], where 0 is the value of \[x\] and 2 is the value of \[y\].
We know that an equation tells us that two sides are equal with some variables and constants and a solution is a value we can put in place of a variable that makes the equation true, that is, the left hand side is equal to the right hand side in the equation.
Replacing 0 for \[x\] and 2 for \[y\] in the left hand side of the equation (1), we get
\[
   \Rightarrow 0 - 2\left( 2 \right) \\
   \Rightarrow 0 - 4 \\
   \Rightarrow - 4 \\
 \]
Since we have that the right hand side value of the equation is 4, but our left side value is \[ - 4\], \[ - 4 \ne 4\].
Therefore, LHS is not equal to RHS.
Hence, \[\left( {0,2} \right)\] is not a solution of the given equation..

Note: While solving these types of questions, students should know that if you are asked to check the solution, we will prove that the left hand side is equal to the right hand side in the equation. Students forget to check the answer, which is an incomplete solution for this problem.