Question

How do you solve the system of equations `3x - 4y = 9` and `8x + 6y = - 2`?

Answer 1

In the first part there is a lot of detail. Not so in the following parts.

I get: `x=23/25`

I will let you take over and finish for `y`

Explanation:

The general approach to this type of problem is to change things so that you only have 1 unknown. This can then be solved. Once you 1 of the unknown value you can find the other.

`3x-4y=9" ".................Equation(1)`
`8x+6y=-2" ".............Equation(2)`

Consider `Equation(1)`
Add `color(red)(4y)` to both sides

`color(green)(3x-4ycolor(red)(+4y)" "=" "9color(red)(+4y))`

`3x+0=9+4y`

Subtract `color(red)(9)` from both sides

`color(green)(3xcolor(red)(-9)" "=" "9color(red)(-9)+4y)`

`4y=3x-9`

Divide both sides by `color(red)(4)`

`color(green)(4/(color(red)(4))y" "=" "3/(color(red)(4)) x-9/(color(red)(4)))`

But `4/4=1`

`y=3/4x-9/4" "..................Equation(1_a)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute for `y` in `Equation(2)` using `Equation(1_a)`

`8x+6y=-2" "->" "8x+6(3/4 x-9/4)=-2`

`" "8x+18/4x-54/4=-2`

`" "25/2x=+23/2`

`" "x=2/25xx23/2`

`" "x=23/25`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Select either of equation(1) or (2) and substitute for `x`
I choose equation(2)

`8x+6y=-2" "->" "8(23/25)+6y=-2`

I will let you finish this off