Question

In the equation $4x + y = 10$, if the value of $x$ is increased by $3$, then what would be the effect on the corresponding value of y
A. The value of y is decreased by $12$
B. The value of y is decreased by $2$
C. The value of y is increased by $3$
D. The value of y will be $3$ times as large

Answer 1

Hint: In the above question, first we will write the above equation in such a way that only y will remain in one side and all the other variables and constants should be in the other side. Then, we will replace the value of x by $x + 3$, so that we can analyze the change in the value of y after substitution.

Complete step by step answer:
In the above question, we have given an equation as $4x + y = 10$. Now, we have to increase its value by three and then we have to find the change in the value of y. First, we will transpose $4x$ to the right hand side.
$ \Rightarrow y = 10 - 4x$
Let y as ${y_1}$ before substitution and ${y_2}$ after substitution.
$ \Rightarrow {y_1} = 10 - 4x$
Now, substitute x by $x + 3$.
$ \Rightarrow {y_2} = 10 - 4\left( {x + 3} \right)$
Now, on multiplication
$ \Rightarrow {y_2} = 10 - 4x - 12$
We can also, write it as
$ \Rightarrow {y_2} = {y_1} - 12$
$ \therefore {y_1} - {y_2} = 12$
From the above equation, we can say that ${y_1}$ is greater than ${y_2}$ by $12$. So, the value ${y_2}$ is less than ${y_1}$ or y by $12$ .Hence, the value of $y$ is decreased by $12$.

Therefore, the correct option is A.

Note: If we do not want to analyze, then we can also put any value of x before substitution and the same value after substitution and then we can find the difference between the final value and the initial value. If the difference is positive, then the value is increased and if the difference is negative, then the value is decreased.