Question

How do you solve the following system?: `5x + 2y =1 , 8x-9y= 12`

Answer 1

The solution set is: `S= {33/61, -52/61}`

Explanation:

Just isolate one constant(`x or y`) in one side on the equality and substitute in the other equality:
`5x +2y = 1 => 5x = 1 - 2y => x = (1-2y)/5`

Now, substitute:
`8 * (1-2y)/5 - 9y = 12` In order to take the dividing `5`, multiply the hole equation by `5`:
`cancel(5) * (8-16y)/cancel(5) - 5 * 9y = 60`
`8 - 16y - 45y = 60`
`-61y = 52 => y = - 52/61`

Now, just go back to the first equation and solve it:
`x = (1 - 2*(-52/61))/5 => x = (1 + 104/61)/5 => x = (61/61 + 104/61)/5 => (165/61)/5`
`x = (165/61)/5 = 165/61 * 1/5 = 33/61`

Then, the solution set is: `S= {33/61, -52/61}`