# How do you solve the following system: -x+6y=12, x-2y=4 ?

Jan 11, 2016

x = 12 and y = 4

#### Explanation:

you can solve this type of system of equations by elimination method or by substitution.
In this case the substitution method appears to be appropriate as both equations may be written in terms of x explicitly.

start by labelling the equations. This makes it 'easier' to follow when performing operations on them

-x + 6y = 12 .........(1)

x - 2y = 4 .............(2)

from (1) : x = 6y - 12

and from (2) : x = 4 + 2y

we can now equate the 2 equations since both are now given as equations in x.

hence 6y - 12 = 4 + 2y hence 4y = 16 and y = 4

substitute y = 4 in x = 6y - 12 to get 24 - 12 = 12.

Here is a graphical illustration of the solution:
graph{(y-1/6 x -2)(y-1/2 x + 2) =0 [-40, 40, -20, 20]}