Question

Find the value of \[k\], if \[x = 2\], \[y = 1\] is a solution of the equation \[2x + 3y = k\].

Answer 1

Hint: Here, we will first use that a solution of the given equation 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. So we will substitute the values of \[x\] and \[y\] in the given equation to find the required value.

Complete step-by-step answer:
We are given that the equation is
\[2x + 3y = k{\text{ ......eq(1)}}\]
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 2 for \[x\] and 1 for \[y\] in the left hand side of the equation (1), we get
\[
   \Rightarrow 2\left( 2 \right) + 3\left( 1 \right) \\
   \Rightarrow 4 + 3 \\
   \Rightarrow 7 \\
 \]
Since we have that the right hand side value of the equation is equal to the left side value \[k\] in the equation (1), so we will find the value of \[k\].
\[
   \Rightarrow 7 = k \\
   \Rightarrow k = 7 \\
 \]
Therefore, 7 is the value of \[k\].

Note: While solving these types of questions, students should know that if you are given the solution, then the left hand side is equal to the right hand side in the equation after substituting the value of the given variables. Students forget to check the answer, which is an incomplete solution for this problem.