Choose a language: English | Malayalam

Algebra (Intermediate) - Solving Simultaneous Equations
 
Method for Solving Simultaneous Equations | Checking Your Answer | Important Note
 
Method for Solving Simultaneous Equations

Dealing with simultaneous equations requires the solving of two equations at the same time, as in the example below.

Solve: 2x + y = 1
  6x - 2y = 13

1. Make the number in front of x or y the same by multiplying.

  2x + y = 1

(multiply by 2)
Multiplying the first equation by 2 gives us
 

4x + 2y = 2

We still have 6x – 2y = 13


2. Get rid of the chosen term by adding or subtracting the two equations.

  4x + 2y = 2  
  6x – 2y = 13  
  10x       = 15 (in this case, the two are added – see note below)


3. Now solve for x.

 
x = 15
  
 
10
  
 
x = 1.5
  


4. Substitute x = 1.5 into either of the equations.
 

             2x + y = 1

 

  (2 x 1.5) + y = 1

 

 
3 + y = 1

 

 
   y = –2
  

Answer: x = 1.5  
  y = – 2  

 
Checking Your Answer

This may be done by substituting x = 1.5 and y = –2 into the other equation, as below, and see that it works:
                  6x – 2y = 13
(6 x 1.5) – (2x – 2) = 13
                  9 - (–4) = 13
                      9 + 4 = 13

 

Important Note

We subtract the two equations to get rid of the chosen term when the signs of the chosen terms are the same.

You can remember this by thinking of SSS (Same Signs Subtract)

3x + 2y = 16    
2x + 2y = 14    
x

 = 2

   (subtract the equations)


Where signs are different, we must add the equations in order to get rid of the chosen term.

You can solve these equations by plotting the two graphs. The solution is the co-ordinates of the point where the two lines meet (refer to later study note on graphs).