Question

How do you solve the following linear system: # x + 3y= 8, 2x + y = 15 #?

Answer 1

`color(blue)(x=37/5" ; "y=1/5)`

Explanation:

Given:
`x+3y=8`............................(1)
`2x+y=15`..........................(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The most straight forward way of dealing with this one is to make the coefficients of y the same and then subtract so that you only have 1 variable.

Multiply equation (2) by 3 then subtract, giving:

`6x+3y=45......................(2_a)`
`underline(color(white)(.)x+3y=8).........................(1)`
`5x+0color(white)(.)=37`

Divide both sides by 5 giving:

`color(blue)(x=37/5)`................................(3)
'~~~~~~~~~~~~~~~~~~~~~~~~
Substitute for `x` in equation (1)

`37/5+3y=8`

Subtract `37/5` from both sides

`3y=8-37/5 = 3/5`

Divide both sides by 3

`color(blue)(y=1/5)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check:
`color(brown)(x+3y=8)color(green)(-> 37/5+3(1/5) = 8) color(red)( " True")`

`color(brown)(2x+y=15)color(green)(->2(37/5)+1/5=15)color(red)(" True")`