Question

How do you solve `4x-12y=5` and `-x+3y=-1` using substitution?

Answer 1

No soluion.

Explanation:

In substitution method we get the value of one variable in term of other from one equation and then put it in another equation.

Here in second equation, transposing `x` term to RHS and constant term to LHS gives us `3y+1=x` or `x=3y+1`. Now putting this in first equation we get

`4(3y+1)-12y=5` or

`12y+4-12y=5` or `4=5`, which is not true and hence we have no solution.

Additional fact - This means that if we draw two lines on a Cartesian plane, they lead too two parallel lines and hence no solution. Had it been `0=0`, it would have been two coincident lines and hence infinite solutions.