Question

X-y=5 4x+y=10 x=? y=?

Answer 1

The solution of the system of linear equations is
`x = 3` and
`y = -2`.

Explanation:

Let
`x - y = 5` and
`4\cdot x +y = 10` expressions of the system of linear equations. Since the number of variables and equations are the same, there is only one solution and we can solve it by algebraic means:

`x-y = 5` (1)

`4\cdot x + y = 10` (2)

From (1):

`x = 5+y`

By applying (1) in (2):

`4\cdot (5+y) +y = 10`

`20+5\cdot y = 10`

`5\cdot y = -10`

`y = -2`

By (1):

`x = 5-2`

`x = 3`

The solution of the system of linear equations is
`x = 3` and
`y = -2`.