# What is solution to the system of equations 2y - x = 4 and  6y - 12= 3x?

##### 1 Answer
Jul 16, 2016

There is no unique solution. Infinitely many solutions are possible.

#### Explanation:

There are many ways of solving simultaneous equations, so it is a case of deciding which method is best for each question.

Each of the equation can be written in a different form.
I am going to change them to have x as the subject.

$2 y - x = 4 \text{ }$ and $\text{ " 6y - 12= 3x " } \div 3$

$x = 2 y - 4 \text{ } 2 y - 4 = x$

Now we see that both equations are the same. In order to solve simultaneous equations, we must have two DIFFERENT equations.

There is therefore not one unique solution, but an infinite number of possible solutions.