Question

If $2x + y = 5$ , then $4x + 2y$ is equal to?
A) 5
B) 8
C) 9
D) 10

Answer 1

Hint: The problem demands comparison and analysis. Compare the two equations and multiply by a suitable factor to make it equal.

Complete step by step answer:
The given equation is
$2x + y = 5......(1)$
It is a linear equation in 2 variables.

The value of $4x + 2y$ is to be determined, which is also a linear equation in two variables.
 If the expression $4x + 2y$ is compared with equation (1), then it is clear that if 2 is multiplied in equation (1), it gives the value of the required expression.

Multiply equation (1) by 2,
$
  2\left( {2x + y} \right) = 2 \times 5 \\
  4x + 2y = 10 \\
$

Hence, the required value of the expression $4x + 2y = 10$.
Thus, the correct option is (D)

Note:
 The problem requires analysis and comparison of the two equations given. A suitable factor is to be chosen based on the analysis.
If 3 is multiplied in equation (1), then it gives the value of $6x + 3y$ as:
$
  3\left( {2x + y} \right) = 3 \times 5 \\
  6x + 3y = 15 \\
$

If 2 is taken out from the required expression
$
  4x + 2y \\
  2(2x + y)......(i) \\
$

The value of $2x + y = 5$ , substitute it in equation (i)
$4x + 2y = 2(5) = 10$
Hence, the value can be calculated in this way also.