# How do you solve the system using the elimination method for 9x - 6y = 12 and 3x - 2y = 20?

Jun 28, 2018

The system is impossible.

#### Explanation:

To solve a system using elimination, you manipulate one of the equations until one of the variables have the same coefficient (in absolute value) in both equations.

Then, you add or subtract the two equations in order to cancel that variable.

For example, let's focus on the $x$ variable. It has coefficient $9$ in the first equation, and $3$ in the second. So, if we multiply the second equation by $3$, the $x$ variable will have coefficient $9$ in both equations.

When we multiply the second equation by $3$, it becomes

$9 x - 6 y = 60$

Now, if we subtract the two equations, we have

$\left(9 x - 6 y\right) - \left(9 x - 6 y\right) = 12 - 60$

which shows that the system is impossible, since it leads to

$0 = - 48$