Question

How do solve the following linear system?: `2x+6y=5 , 8x+2y=2`?

Answer 1

`=> x= 13/44` and `y=9/11`

Explanation:

Use the Substitution method to solve this problem.
Consider the first equation.

`2x=5-6y`
`=> 8x= 20-24y` (multiplying LHS and RHS by 4)
Now insert the value of 8x into the second equation to get:
`(20-24y) + 2y=2`
`=> 20-22y=2`
`=> 22y=18`
`=>y=18/22` i.e.`y=9/11`

Now insert the value of y in any of the two given equations.

Inserting it into the second equation, we get
`8x + 18/22=2` ( Since 2y=`18/22`)
`=> 8x= 26/22`
`=> 4x= 13/11`
`=> x= 13/44`