Question

How do solve the following linear system?: `3x-8y=6, 5x+2y=2`?

Answer 1

See a solution process below

Explanation:

`3x - 8y = 6 - - - eqn1`

`5x + 2y = 2 - - - eqn2`

Using elimination method..

`5 xx (3x - 8y = 6)`

`3 xx (5x + 2y = 2)`

`15x - 40y = 30 - - - eqn3`

`15x - 6y = 6 - - - eqn4`

Subtract `eqn3 and eqn4`

`-34y = 24`

`y = - 24/34`

`y = - 12/17`

Substitute the value of `y` into `eqn1`

`3x - 8y = 6`

`3x - 8(-12/17) = 6`

`3x + 96/17 = 6`

Multiply through by `17`

`17(3x) + 17(96/17) = 17(6)`

`51x + 96 = 102`

`51x = 102 - 96`

`51x = 6`

`x = 6/51`

`x = 2/17`

Hence;

`x = 2/17 and y = -12/17`