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

Last updated date: 20th Jun 2024
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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.

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.