We will use elimination to solve this linear system.
Firstly we need to get same numbers but opposite sign from that same number.
In x + 6y=28 /* (-6) (multiply the first equation with -6)
6x-5y=-1
We get,
color(blue)(-6x)-36y=-168 ------- color (red) (equation 1
color(blue)(6x)-5y=-1 ------ color(blue)(equation 2)
You can see that -6x and 6x are opposites so we cancel them but firstly write the following,
cancel(-6x)-36y+cancel(6x)-5y=-168-1
-41y=-169 From here
y=-169/-41
y=169/41
It's now
-6x-36y=-168 ------- color (red) (equation 1
y=169/41 ------ color(blue)(equation 2)
Basically just add y=169/41 into y in the first equation
-6x-36*169/41=-168
-6x-6084/41=-168
-6x=-168+6084/41
-6x=-804/41
x=(804/41)/(6/1)
x=cancel804/cancel246
x=134/41
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Final result:
x= 134/41
y=169/41
