Question

Check whether the following is the solution of the equation \[x - 2y = 4\] or not: \[\left( {4,0} \right)\].

Answer 1

Hint: Here in this question, we have to check whether the given point is the solution of the equation. The given equation in the form of equation of straight line or linear equation i.e., \[y = mx + b\] to solve this, substitute the $x$ and $y$ values of point in the equation when simplifying it satisfies the condition \[LHS = RHS\] then it’s a solution of the equation otherwise not a solution.

Complete step by step solution:
The given equation is a linear equation. These equations are defined for lines in the coordinate system. An equation for a straight line is called a linear equation. The general representation of the straight-line equation is \[y = mx + b\], it involves only a constant term and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, this equation is called a "linear equation of two variables," where y and x are the variables.
Consider the given equation
\[ \Rightarrow \,\,\,\,x - 2y = 4\]------(1)
We have to check if the given point \[\left( {4,0} \right)\] is a solution of the equation or not.
Substitute the value of \[x = 4\] and \[y = 0\] in equation (1), then
\[ \Rightarrow \,\,\,\,\left( 4 \right) - 2\left( 0 \right) = 4\]
On simplification, we get
\[ \Rightarrow \,\,\,\,4 - 0 = 4\]
\[ \Rightarrow \,\,\,\,4 = 4\]
Therefore, \[LHS = RHS\]
Hence, the point \[\left( {4,0} \right)\] is the solution of the linear equation \[x - 2y = 4\].

Note:
The algebraic equation or an expression is a combination of variables and constants, it also contains the coefficient. The solution of the equation means when Both sides of the equation are supposed to be balanced for solving a linear equation. Equality sign denotes that the expressions on either side of the ‘equal to’ sign are equal. Since the equation is balanced, for solving it certain mathematical operations are performed on both sides of the equation in a manner that it does not affect the balance of the equation.