Question

Choose the correct option from the given options by solving the following questions:
If \[3y = y + 2\], calculate the value of \[2y.\]
A. \[1\]
B. \[2\]
C. \[3\]
D. \[4\]

Answer 1

Hint: Bring all the variables to one side of the equation and all the constants to one side of the equation. By using simple linear algebra and its properties, we calculate the value of the variable once we get the value of the variable, we substitute that value in the given expression of the question to get the final solution.

Complete step-by-step solution:
Given equation,
\[3y = y + 2\]
Now, the variable here is \[y\].
Let us bring all the \[y\] terms to one side, that is the left-hand side of the equation and the constant terms to the right side of the equation.
\[y\]on the right-hand side when taken to the left-hand side becomes \[ - y\].
And the constant which is on the right-hand side remains on the right-hand side.
\[3y - y = 2\]
Now, we subtract the variable terms using the simple algebraic properties. Since the term is uniform and we can subtract, we get;
\[2y = 2\] we have the answer to the asked question here. But to find the value of the variable, go ahead.
Now, we have to divide the left-hand side and the right-hand side with the constant to eliminate the constant and get the single value of the variable.
\[\dfrac{{2y}}{2} = \dfrac{2}{2}\]
That implies, the divisible numbers get cancelled. We get;
\[y = 1\]
Now that we got the value of \[y\], we substitute it in the asked question.
\[2y = 2(1) = 2\]
Therefore, we have the value, \[2y = 2\].

The correct option is B.

Note: We have to mind that, the equation is a linear equation which is expressed in the form of one variable as \[ax + b = 0\] where \[a\] and \[b\] are two integers which are coordinates of the variable. This equation is a one-degree variable which is why we can perform linear algebraic operations.