Question

To eliminate x from equations x + y + 3x = 12 $ \to $….(1) and 8x + 3y = 17 $ \to $….(2), equation (2) is to be multiplied by
A. 8
B. $ - \dfrac{1}{2}$
C. $\dfrac{1}{2}$
D. 3

Answer 1

Hint: In this question, elimination method will be used in order to eliminate the required variable from the given equations in two variables, using this information will help us to approach the solution of the question.

Complete step-by-step answer:
Given equations are x + y + 3x = 12 $ \Rightarrow $4x + y = 12$ \to $….(1) and 8x + 3y = 17 $ \to $(2)
Now, in order to eliminate x from equations (1) and (2), the coefficient of x in both the equations should be the same so that we will multiply equation (2) by $\dfrac{1}{2}$.
Therefore, equation (2) becomes
$4x + \dfrac{{3y}}{2} = \dfrac{{17}}{2}$ (equation 3)
Now, x can be easily eliminated by simply subtracting equation (3) from equation (2)
We get $4x - 4x + \dfrac{{3y}}{2} - y = \dfrac{{17}}{2} - 12$
$y = - 7$
So, now the obtained equation has only variable y
Therefore, in order to eliminate x from equations (1) and (2), equation (2) is to be multiplied by $\dfrac{1}{2}$.

So, the correct answer is “Option C”.

Note: In these types of problems, we have to make the coefficient of the variable (which needs to be eliminated) in the two given equations equal by multiplying or dividing with any number in one equation so that when the two equations be subtracted from each other that particular variable is eliminated.