Question

How do you solve the system of equations `6x-4y=24` and `5x+10y=30` by elimination?

Answer 1

`x=9/2`
`y=3/4`

Explanation:

`6x-4y=24`
or
`2(3x-2y)=24`
or
`3x-2y=24/2`
or
`3x-2y=12`------------Eq.`A`

`5x+10y=30`
or
`5(x+2y)=30`
or
`x+2y=30/5`
or
`x+2y=6`--------------Eq. `B`
Adding up Eq.`A` and `B`
We get
`3x-2y+x+2y=12+6`
or
`4x+0=18`
or
`4x=18`
or
`x=18/4`
or
`x=9/2`----------------------Ans `1`
By putting the value `x=9/2` in the equation `x+2y=6`
We get
`9/2+2y=6`
or
`2y=6-9/2`
or
`2y=3/2`
or
`y=3/4`--------------------------Ans `2`

Answer 2

`x = 4 1/2, y = 3/4`

Explanation:

Neither of these equations is in simplest form. Let's do that first:

`6x-4y =24 " "div 2 rArr " "3x -2y = 12 .....................A`
`5x +10y = 30" "div 5 rArr" "x+2y = 6.......................B`

`color(white)(..............)3x color(red)(-2y) = 12 .....................A`
`color(white)(................)xcolor(red)(+2y) = 6.......................B`

`A+B color(white)(............)4x=18" "` (y-terms have been eliminated)

`color(white)(........................) x = 4 1/2`

Subst into B: `4 1/2 + 2y = 6`

`color(white)(................) 2y = 6- 4 1/2 = 1 1/2`

`color(white)(...................)y= 3/4`