Question

How do you solve the following system: `4x+y=-7, 8x-y=19`?

Answer 1

The Soln. `: x=1, y=-11`

Explanation:

From the First eqn., we get `:y=-7-4x........(i)`

Sub.ing this `y` in the second eqn., we get,

`8x-(-7-4x)=19`

`rArr 8x+7+4x=19`

`rArr 12x=19-7=12`

`rArr x=12/12=1`

Then, by `(i), y=-7-4=-11`

Hence the Soln. `: x=1, y=-11`

Answer 2

`x = 1 " and " y = -11`

Explanation:

Each of these equations can easily be written with `y` as the subject.

`y = -4x -7 " and " y = 8x-19`

Because `y=y` we can equate the expressions.

`8x -19 = -4x -7`

`12x = 12`

`x = 1`

There are now two equations for finding the value of `y`. It is a good idea to substitute the `x` value into both, to check that our answers are correct.

`y = -4(1) -7 " and " y = 8(1)-19`

`y = -11 " "y = -11`