Question

What is the value of two numbers if their sum is 12 and their difference is -4?

Answer 1

Hint: For solving this question you should know about the general solution of two or more than two equations. It is completely dependent on the general mathematical calculation of the equation. In this firstly we will consider two variables and then will make the equations of sum and the difference of both and then solve these for getting the value of numbers.

Complete step by step solution:
According to the question we have to find those two numbers which are 12 if we add them and they will -4 if we subtract them.
So, for this calculation we will consider two variables x and y and set them according to the question. The question said that the sum of these is equal to 12. So, we can write that: \[x+y=12-\left( 1 \right)\]
And the difference of both is equal to the -4.
So, we can write it as \[x-y=-4-\left( 2 \right)\]
So, we have now two equations which will be sufficient according to the question. And we have also found the value of two variables x & y and two equations are sufficient to calculate the value of these two variables.
Now, if we take equation (1) and (2) and add them with one another, then:
Equation (1) + Equation (2)
\[\Rightarrow \] \[\begin{align}
  & x+y=12 \\
 & \underline{+x-y=-4} \\
 & 2x=8 \\
\end{align}\]
\[\begin{align}
  & x=\dfrac{8}{2} \\
 & x=4 \\
\end{align}\]
So, the one variable x is equal to 4.
Now, if we want to calculate the value of another variable then we have to put this value in any one equation and then solve that:
So, we put \[x=4\] in equation (1).
\[\begin{align}
  & \Rightarrow 4+y=12 \\
 & \Rightarrow y=12-4 \\
 & \Rightarrow y=8 \\
\end{align}\]
So, the two numbers are 4 and 8.

Note: During solving this type question we have to be careful with the equations. We have to assure that the given number of equations are equal to the given number of variables whose value has to find us. And if any variable is extra in the equation then we can’t determine that.