# If $2x + y = 5$ , then $4x + 2y$ is equal to?

A) 5

B) 8

C) 9

D) 10

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**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.