Question

If (2,0) is a solution of linear equation \[2x+3y=k\] then the value of \[k\] is:
A). \[4\]
B). \[5\]
C). \[2\]
D). \[1\]

Answer 1

Hint: In this question we have given a linear equation and its solution and we have to find the value of the variable \[k\], hence to find the value of \[k\] we need to put the value of the given solution in the linear equation so that we could obtain the given result after that check which option is correct in the given options.

Complete step-by-step solution:
An equation is made up of variables, which are usually English alphabets that can take any real value and yet satisfy the equation. Constants and coefficients are also included. The coefficients are the numbers related with the variables, while the constants are the variable independent numbers in the equation. The algebraic equations having the order of unity or one are known as linear equations. Linear equations are first-order equations. In the coordinate system, these equations are defined for lines. A linear equation is an equation for a straight line.
Finding the value of a variable for which the equation becomes true is known as finding the solution of a linear equation. For each variable in a linear equation, there is usually only one solution. Inverse Mathematical techniques are employed to solve linear equations in one variable.
Linear equations are equations in which the variables have been increased to the power of one. Based on the number of variables in the equation, linear equations are divided into distinct categories. The following are the various types of linear equations:
1. One-variable linear equations are linear equations that have only one variable.
2. Linear equations with two variables are linear equations that have two variables.
3. Three-variable linear equations are linear equations with three variables.
Now according to the question:
If \[(2,0)\] is a solution of the linear equation \[2x+3y=k\]
Therefore the value of \[x\] is \[2\] and the value of \[y\] is \[0\]
Hence put the value of \[x\] and \[y\] in the given linear equation so that we can get the value of \[k\] :
\[\Rightarrow 2x+3y=k\]
\[\Rightarrow 2\times 2+3\times 0=k\]
\[\Rightarrow 4+0=k\]
\[\Rightarrow k=4\]
Hence option \[(A)\] is correct as the value of \[k=4\].

Note: Students do you know that in a linear equation or inequality, the highest exponent of the variable is one. When plotted on a graph, one variable linear equations are straight lines. For straight lines, a linear equation is used. A straight line is not formed by a nonlinear equation. It could be a curve with a changing slope value.