Question

How do you solve \[3m+n=2\] and \[m-2n=3\] using substitution?

Answer 1

Hint: In this problem, we have to solve and find the value of m and n using substitution. We can first multiply number 2 to the first equation, so that we can get similar terms to be cancelled in the elimination and we will get one of the values of m or n. we can then substitute the resulted value in one of the equations to get the other unknown variable value.

Complete step by step answer:
We know that the given equations to be solved is,
\[3m+n=2\]……. (1)
\[m-2n=3\]……. (2)
We can now multiply the number 2 on both sides of the equation (1), we get
\[\Rightarrow 6m+2n=4\]…… (3)
Now we can add the equation (2) and (3), so that we can get similar terms to be cancelled in the elimination and we will get one of the values of m or n.
\[\Rightarrow 6m+2n-4+m-2n-3=0\]
Now we can simplify the above step, we get
\[\begin{align}
  & \Rightarrow 6m+m-4-3=0 \\
 & \Rightarrow 7m-7=0 \\
 & \Rightarrow m=1 \\
\end{align}\]
Now we can substitute the above value in the equation (2) and simplify, we get
\[\begin{align}
  & \Rightarrow 1-2n=3 \\
 & \Rightarrow -2n=2 \\
 & \Rightarrow n=-1 \\
\end{align}\]
Therefore, the value of m = 1 and the value of n = -1.

Note:
Students make mistakes while multiplying numbers to the equation in order to get similar terms to be cancelled to get any one of the values, which we can substitute to get the other value. We can substitute the first resulted value in any of the given equations to get the other value. We can substitute the resulting values in the equation to check whether the values are correct.
We can substitute m = 1 and n = -1 in the equation (1),
\[\begin{align}
  & \Rightarrow 3\left( 1 \right)-1=2 \\
 & \Rightarrow 3-1=2 \\
\end{align}\]
Therefore, the values are correct.