Answer: The correct option is (C) 2.
Step-by-step explanation: We are given to find the difference of the values of the two variables in the following system of linear equations :
[tex]y=2x+1~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+3y=10~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Substituting the value of y from equation (i) in equation (ii), we get
[tex]x+3y=10\\\\\Rightarrow x+3(2x+1)=10\\\\\Rightarrow x+6x+3=10\\\\\Rightarrow 7x=10-3\\\\\Rightarrow 7x=7\\\\\Rightarrow x=\dfrac{7}{7}\\\\\Rightarrow x=1.[/tex]
From equation (i), we get
[tex]y=2\times 1+1=2+1=3.[/tex]
So, the values of the variables are x = 1 and y = 3.
Therefore, the difference in the values of the variables is given by
[tex]D=y-x=3-1=2.[/tex]
Thus, the required difference in the values of teh variables is 2.
Option (C) is CORRECT.
