Question

How do you solve the following system?: `8x +6y =9 , - 5x -7y = -2`

Answer 1

With some arrangement. `x=51/26` and `y=-29/26`

Explanation:

Expand the first equation with term 5
Expand the second equation with 8.

Now you have:

`40x+30y=45`
`-40x-56y=-16`
Now sum these up:
`-26y=29`

or `y=-29/26`

Now you can find x using the first or second equation:

`8x-(6*29)/26=9`

`8x=9+(6*29)/26`

`8x=(117/13) + ((3*29)/13)`

`8x=204/13`

`x=204/104`

or

`x=51/26`

Answer 2

`x = 1 25/26`, `y = -1 21/182`

Explanation:

`8x + 6y = 9` ....................(i)
`-5x - 7y = -2` ....................(ii)

You can solve this system by using Elimination method.

You can eliminate either `x` or `y` here.
I will eliminate `x`.

So multiplying eq.(i) by `+5` and eq(ii) by `+8`, you will get

`40x + 30y = 45` ......................(iii) &
`-40x - 56y = -16` ........................(iv)

Adding eq (iii) and (iv), you will get

`-26y = 29`

`rArr` `y = -29/26`

Substituting `y = -29/26` in eq(i), you will get

`8x + (-29/26)*6 = 9`

`rArr` `8x = 9 + 87/13`

`rArr` `8x = (117 + 87)/13`

`rArr` `8x = 204/13`

`rArr` `x = 204/104 = 51/26`