6x + y = 8 (1)       4x - y = 12 (2)

Method 1 elimination:

-Adding/subtracting the two equations together to eliminate one of the unknowns 

 (1) + (2)

  6x + y = 8

+  4x - y = 12

10x = 20        (/10)

x= 2

sub 'x=2' into (2)

4(2) - y = 12

8 - y = 12      (+y) 

8 = 12 + y     (-12)

-4 = y

Method 2 substitution:

-rearranging one of the equations to make an unknown the subject 

rearrange (2)

4x - y = 12 

4x = y + 12      (+y)

y= 4x - 12        (-12)

sub 'y = 4x - 12' into (1)

6x + '4x - 12' = 8

10x - 12 = 8        (+12)

10x = 20

x = 2

sub 'x=2' into 'y = 4x - 12'

y = 4(2) - 12 

y = 8 - 12

y = -4