Question

How do you solve $ 6m + n = 9 $ and $ m - 8n = 26 $ using substitution?

Answer 1

Hint: In the question, we are provided with two equations. And we had to solve these equations with the help of a substitution method. In this method, find the value of one variable and put that value into the second equation and solve the respective variables.

Complete step by step solution:
In the question, we are provided with two equations. In these equations “m” and “n” are variables and we have to find their values. Writing the equations and marking them for our convenience,
 $ 6m + n = 9 $ $ \ldots \left( 1 \right) $
 $ m - 8n = 26 $ $ \ldots \left( 2 \right) $
Solving the above two equations with the substitution method.
Now, find the value of “n” from the first equation and mark this equation.
 $ n = 9 - 6m $ $ \ldots \left( 3 \right) $
Now, put this value of “n” into the equation $ \left( 2 \right) $
 $ m - 8\left( {9 - 6m} \right) = 26 $
Removing the brackets and taking the variable “m” to the left=hand side and all the constants to the right-hand side. keep in mind while changing the sides, the signs would change.
 $
  m - 72 + 48m = 26 \\
  49m = 26 + 72 \\
   \Rightarrow m = \dfrac{{98}}{{49}} \\
   \Rightarrow m = 2
  $
Now, put this value of “m” into the equation $ \left( 3 \right) $ and find the value of “n”
 $
  n = 9 - 6m \\
     = 9 - 12 \\
     = -3
  $
Hence, the required answer is $ m = 2 $ and $ n = -3 $
So, the correct answer is “ $ m = 2 $ and $ n = -3 $”.

Note: The multiplication is done as $ ( - ) \times ( + ) = ( - ) $ and same as when positive is taken at first term and the other formulas are $ ( + ) \times ( + ) = ( + ),( - ) \times ( - ) = ( + ) $ . While students usually make silly mistakes in taking the signs to the other sign, be careful while calculating.