How do you solve the system of equations #x-2y=6# and #2x-4y=10#?
2 Answers
No solution.
Explanation:
To solve any two pair of linear equations in two variables,one important method is substitution method under which value of one variable in terms of another is taken and is substituted in second equation.
Another method is drawing a graph of two lines and their point of intersection gives the solution.
Here first equation is
But this is contradictory and hence we have no solution. In such a case if we use graphical method and draw graph, we get two parallel lines and hence no solution. One can also say equations are inconsistent.
Note - Some times we may get
The equation cannot be solved and there are no solutions.
Explanation:
Looking at these equations we should realise that there is a problem!
The left hand side of each equation is the same, but the right hand sides are different. Huh???
We cannot do the same operations with the variables, but get two different results.....
Let's solve anyway.
It follows that: if
This tells us that the equation cannot be solved and there are no solutions.