Question

How do solve the following linear system?: `x= y - 11 , y = 4x + 4`?

Answer 1

Soln. is `(x,y)=(7/3,40/3).`

Explanation:

Submit the value of `y,` taken from `2^(nd)` eqn., in the `1^(st)` eqn. to get,

`x=4x+4-11 rArr x-4x=4-11 rArr -3x=-7 rArr x=-7/-3=7/3.`

Hence, by `2^(nd)` eqn., `y=4(7/3)+4=28/3+4=40/3.`

Soln. is `(x,y)=(7/3,40/3).`

Answer 2

`x = 7/3 = 2 1/3 and y = 40/3 = 13 1/3`

Explanation:

There are several methods you can use, but there is a single `y` term in each equation, so equating them is probably the easiest method.

Change the first equation to: `y = x+11`

Now, the y in each equation is the same, so;

if: `" " y = y`
then:`" "4x + 4 = x + 11`

`" "4x - x = 11-4`
`" " 3x = 7`

`x = 7/3 = 2 1/3`

To find the value of `y`, substitute `x = 7/3` into either of the equations above ..... or both, to check that they give the same answer.

`y = 4xx 7/3 +4 = 40/3 " and " y = 7/3 +11 = 40/3`