Question

How do you solve $ x - y = 3 $ and $ 7x - y = - 3 $ ?

Answer 1

Hint: To solve the given equations, first we will separate both the variables of equation (i), one in L.H.S and one in R.H.S . And then substitute in the second equation to find the value of one of the variables and again substitute the found value of variable in equation(i).

Complete step by step solution:
Given equations-
 $ x - y = 3 $ ….eq.(i)
 $ 7x - y = - 3 $ …eq.(ii)
First we will separate variables in eq.(i):
 $
  x - y = 3 \\
   \Rightarrow x = 3 + y \;
  $
Now, we will substitute the value of $ x $ in eq.(ii), then we get-
 $
  7x - y = - 3 \\
   \Rightarrow 7(3 + y) - y = - 3 \\
   \Rightarrow 21 + 7y - y + 3 = 0 \\
   \Rightarrow 6y + 24 = 0 \\
   \Rightarrow 6y = - 24 \\
   \Rightarrow y = - 4 \;
  $
Now, in eq.(i) , we will put the above value of $ y $ to find the values of $ x $ :
 $
  \therefore x - y = 3 \\
   \Rightarrow x - ( - 4) = 3 \\
   \Rightarrow x = 3 - 4 \\
   \Rightarrow x = - 1 \;
  $
Hence, the solution is $ x = - 1,y = - 4 $
In coordinate form:
 $ ( - 1, - 4) $ .
So, the correct answer is “ $ ( - 1, - 4) $ ”.

Note: Steps for applying the substitution method:-
Step-1: Solve one equation for one of the variables.
Step-2: Substitute (plug-in) this expression into the other equation and solve.
Step-3: Resubstitute the value into the original equation to find the corresponding variable.