Question

How do you solve the following system?: `2x +3y =5 , 8x +5y = -4`

Answer 1

`X = 33/16 and Y = 48/14`

Explanation:

Given:
`2x+3y = 5 and 8x + 5y = -4`
We need to make either one of the terms given, have similar coefficients to cancel out.

`(2x + 3y = 5)` x `8`
`color(red)(16x + 24y = 40)`

`(8x+ 5y = -4)` x `2`
`color(red)(16x + 10y = -8)`

Subtracting one from the other, we get:
`16x + 24 y = 40`
`-(16x+10y = -8)`

We get `14y = 48; y =48/14`

Substituting y = `48/14` in any one of the equations.
`2x + cancel(3)(14/cancel(48)) = 5`
`2x + 7/8 = 5`
`2x = 5-7/8`
`2x = (40-7)/8`
`:. x = 33/16`