Question

How do you solve the following linear system: `x + 6y = 28 , 8x - 7y = -3`?

Answer 1

The solution is:
`color(green)(x =178/55`

`color(green)(y=227/55`

Explanation:

`x +6y =28`, multiplying by `8`
`color(green)(8x) +48y =224`......equation `(1)`

`color(green)(8x) -7y =-3`......equation `(2)`

Solving by elimination:
Subtracting equation `(2)` from `(1)`

`cancelcolor(green)(8x) +48y =224`

`-cancelcolor(green)(8x) +7y = 3`

`55y = 227`

`color(green)(y=227/55`

Finding `x` from equation `(2)`:

`8x -7y =-3`

`8x =-3 + 7y`

`8x =-3 + 7 xx227/55`

`8x =-3 + 1589/55`

`8x =-165/55 + 1589/55`

`8x =1424/55`

`x =1424/(55 * 8)`

`color(green)(x =178/55`