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

Apr 27, 2016

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 $3 y + 1 = x$ or $x = 3 y + 1$. Now putting this in first equation we get

$4 \left(3 y + 1\right) - 12 y = 5$ or

$12 y + 4 - 12 y = 5$ 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.