Question

How do you solve it using the elimination method \[x+y=10\] and \[x-y=2\]?

Answer 1

Hint: In this problem, we have to solve the given two equations and find the value of x and y. We are given to solve the equations using elimination methods. We know that in the elimination method we can add or subtract the given equations to eliminate one of the unknown variables, i.e. y in this problem and find the value of x. We can then substitute the value of x in any of the equations to get the value of y.

Complete step by step answer:
We know that the given two equations to be solved are,
\[x-y=2\]…… (1)
\[x+y=10\] ……. (2)
We can now add both the equation, in order to eliminate anyone of the variables, we get
\[\Rightarrow x-y-2+x+y-10=0\]
We can now simplify the above step by cancelling the similar terms with opposite sign and add the remaining terms, we get
\[\begin{align}
  & \Rightarrow 2x=12 \\
 & \Rightarrow x=6 \\
\end{align}\]
The value of x = 6.
We can now substitute the value of x in the equation (1), we get
\[\begin{align}
  & \Rightarrow 6-y=2 \\
 & \Rightarrow y=4 \\
\end{align}\]

Therefore, the value of x = 6 and y = 4.

Note: Students make mistakes while eliminating the similar terms with opposite signs, in this problem we have given a simple equation, if we are given a different equation, we have to multiply some terms to make it similar for the elimination. We can now see whether the resulting values are correct.
We can substitute x = 6 and y = 4 in (1) and (2), we get
\[\begin{align}
  & \Rightarrow 6-4=2 \\
 & \Rightarrow 6+4=10 \\
\end{align}\]
Therefore, the values are correct.