Question

How do you solve \[3a+b=4\] and \[a-2b=6\] using substitution?

Answer 1

Hint: In this problem, we have to solve and find the values of a and b form the given two equations using substitution. We can first multiply the number 2 to the first equation to simplify the equations by elimination method. We will get any of the values of a or b, which we can substitute in any of the equations to get the other value.

Complete step by step solution:
We know that the given equations to be solved is,
\[3a+b=4\]……. (1)
\[a-2b=6\]……. (2)
We can now multiply the number 2 on both sides of the equation (1), we get
\[\Rightarrow 6a+2b=8\]…… (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.
\[\Rightarrow a-2b-6+6a+2b-8=0\]
Now we can simplify the above step, we get
\[\begin{align}
  & \Rightarrow 6a+a-6-8=0 \\
 & \Rightarrow 7a-14=0 \\
 & \Rightarrow a=2 \\
\end{align}\]
Now we can substitute the above value in the equation (2) and simplify, we get
\[\begin{align}
  & \Rightarrow 2-2b=6 \\
 & \Rightarrow -2b=4 \\
 & \Rightarrow b=-2 \\
\end{align}\]
Therefore, the value of a = 2 and the value of b = -2.

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 also apply the resulting values in any of the equations, to check whether the values found are correct.
We can substitute the value a = 2, b = -2 in equation (2), we get
\[\begin{align}
  & \Rightarrow 2-2\left( -2 \right)=6 \\
 & \Rightarrow 4+2=6 \\
\end{align}\]
Therefore, the values are correct.