Solving Linear Equations by Substitution Method

When we are solving a system of equations, which has two or more unknown variables, we use the method of substitution.  In this method, we should isolate one of the variables in one of the euqations and then substitute the results in the other equation.  If there are two unknown variables, then there should be atleast two equations to solve the variable.

 

Examples on substitution method.

 

Worked  examples on substitution method.

Example: 2x-9y = 1 
          x-4y = 1   

Step 1: Name these equations as  
    2x - 9y = 1--------(1) 
         x - 4y = 1--------(2)

Step 2: Isolate equation x in equation (2) 
                 x = 1 + 4y-------(3) name this equation as (3)

(when you move -4y to the other side of the equals '=' sign, it becomes a + 4y)

Step 3:  Substitute the new equation(3) in (1)
                                  2x - 9y = 1                                  
                  2 ( 1+ 4y) - 9y = 1

Step 4: Next simplify to get       2 + 8y - 9y = 1   
                   2 - y = 1

now move 2 to the other side of the equals '=' sign, and it becomes - 2

                                  -y = 1 - 2  
on simplifying we get             -y = -1

Now since, it is negative -y,just multiply both the sides by - 1 to get y = 1    

Step 5: Now that we have got the value of y, plug in that value in any equation (1) or (2)

                        Let us consider equation (2) and lets plug in the value of y = 1
                                x - 4y = 1                                
                                x- 4(1) = 1                                
                                x- 4 = 1                                

on moving -4 to the other side, it becomes + 4
                                x = 4+ 1                              
                        Hence,  x = 5    

On solving these two above given equations, we got the value of x as 5 and y as 1.

Check:  we can also verify if the answers we have obtained is right or not by substitute  in the value of x and y which 

we obtained in any of those two equations.

                 Let us consider      x -4y = 1                                 
                    5 - 4(1) = 1
                                    5- 4 = 1                                  
                    1= 1
                            right hand side = left hand side.

Hence, we can say that the answer x = 5 and y = 1 which we obtained is correct .

So, this is about substitution method. 

 

Practice problems on substitution method

 

Solve by substitution method.

1) x + y = -4
    x - y = 2

2) x + y = 10
   y = x + 8

3) 3x + y = 5
   4x - 7y = -10

4) y - 2x = -5
  3y - x = 5