Question

How do you solve the following system of equations?: `13x+3y=16, 7x-5y=69`?

Answer 1

`x =287/86 ; y=-785 /86`

Explanation:

`13x+3y=16` ----------(1)
`7x -5y =69`----------(2)

Multiply `eq^n` (1) by 5 and `eq^n` (2) by 3 we get,

`65x+15y=80` ----------(3)
`21x -15y =207`----------(4)

Add the `eq^n` (3) and `eq^n` (4)

`[65x+15y=80] + [21x -15y =207]`

`65x+21x +15y-15y = 80+207`

`86x = 287`

`x =287/86`

Substitute in `eq^n (1)`

`13x+3y=16`

`13(287/86)+3y=16`

`3731/86 +3y =16`

`3y = 16-3731/86`

`3y = (1376-3731)/86`

`3y= -2355/86`

`y= -2355/(86xx3)`

`y=-785 /86`