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# For a pair of equations $2x + 3y = 10$ and $3x - y = 4$, $x = ................$A) 2B) -20C) 10D) -10

Last updated date: 14th Aug 2024
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Hint:Here we will use the elimination method to solve the two given linear equations and then evaluate the value of x.

In elimination method, we have to make the coefficient of one of the variable in both the equations and then add or subtract the equations to eliminate that variable and find the value of another variable.
Step by step solution:-
The given linear equations are:-
$2x + 3y = 10$………………………..(1)
$3x - y = 4$…………………………………(2)
Here we will use the elimination method to eliminate the variable y and then evaluate the value of x.
Hence we will first multiply equation 2 by 3.
On multiplying we get:-
$3 \times \left( {3x - y = 4} \right)$
Solving it further we get:-
$3 \times 3x - 3 \times y = 3 \times 4 \\ \Rightarrow 9x - 3y = 12.........................(3) \\$
Now since the coefficient of y is same in equation 1 and equation 3
Hence we can eliminate the variable y by adding equations 1 and 3
Hence adding equation 1 and 3 we get:-
$2x + 3y = 10 \\ 9x - 3y = 12 \\ \cdots \cdots \cdots \cdots \cdots \cdots \cdots \\ 11x + 0 = 22 \\$
Now calculating the value of x we get:-
$11x = 22$
Dividing whole equation by 11 we get:-
$x = \dfrac{{22}}{{11}} \\ \Rightarrow x = 2 \\$
Hence the value of x is 2

So, the correct answer is “Option A”.

Note:Student should note that in elimination method the coefficient of at least one variable should be the same to eliminate that variable.Also, the value of the variable obtained by elimination can be substituted in any of the given equations to get the value of the other variable.