Question

What is the difference of the values of the two variables in this system of equations? y = 2x + 1 x + 3y = 10 A. 0 B. 1 C. 2 D. 3

Answer 1

B would be the answer

Answer 2

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 :

$y=2x+1~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+3y=10~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Substituting the value of y from equation (i) in equation (ii), we get

$x+3y=10\\\\\Rightarrow x+3(2x+1)=10\\\\\Rightarrow x+6x+3=10\\\\\Rightarrow 7x=10-3\\\\\Rightarrow 7x=7\\\\\Rightarrow x=\dfrac{7}{7}\\\\\Rightarrow x=1.$

From equation (i), we get

$y=2\times 1+1=2+1=3.$

So, the values of the variables are x = 1  and  y = 3.

Therefore, the difference in the values of the variables is given by

$D=y-x=3-1=2.$

Thus, the required difference in the values of teh variables is 2.

Option (C) is CORRECT.