System of linear equations

Thread Starter

sadaf

Joined Aug 4, 2010
25
Below there are two equations;

1. 2x+3y=4
2. 4x+6y=8

can these equations have any solution?
if it is then what is the solution and what is the common point where they meet?
please tell me i am so confused...
 

debjit625

Joined Apr 17, 2010
790
No,this cant have any solution
Now using determinants we could determine if it could have any solution its like this
Example
ax + by = c
dx + ey = f
if (a*e) - (d*b) != 0 i.e.. not equal to zero then the system of linear equation have a unique solution.
In your case
(2*6) - (4*3) = 0 so it will not give you a unique solution

Good luck
 

Papabravo

Joined Feb 24, 2006
21,158
The other way to see this is to recognize that both equations are essentially the same. If you multiply both sides of the first equation by 2 you get the second equation. Hence the equations are not independent and therefore have no unique solution. Both equations represent the same line and so they have an infinite number of points in common.
 
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