Question

How do you solve this set of linear equations `2x - 3y = - 10; 5x + 6y = 12?`

Answer 1

`x = -8/9 and y = 2 20/27`

Explanation:

When working with a system of linear equations, the best scenario is to create additive inverses with one of the variables.
They ADD together to give 0.

(`-6x+6x = 0`) or (`+11x-11x = 0`)

`color(white)(xxxxxxxx)2x-3y =-10`...........................A
`color(white)(xxxxxxxx)5xcolor(red)(+6y) =" "12`.............................B
`Axx2:" "4xcolor(red)(-6y) = -20` ..............................C
`B+C" "9x" "= -8" "larr` no y term

`color(white)(xxxxxxxxxxxx)x = -8/9" "larr` the value of x

`x=-8/9 " in " A:" "2(-8/9) -3y = -10`

`-16/9 -3y = -10`

`-1 7/9 +1 0= 3y`

`8 2/9 = 3y`

`74/27 = y`

`y = 2 20/27`