Question

How do you solve the following linear system: # x + y = 6 , x = y + 2 #?

Answer 1

Substitute `x` by using `y` or vice versa.
Solve it like a normal equation
Solve for the other variable

Explanation:

`1: x + y = 6`
`2: x = y + 2`

The second equation helps us a lot here, since `x` is isolated from `y` and the constant. The second equation states that `x` can be written as `y + 2`, since `x = y + 2`. Put this expression into equation number 1.

`1: color(red)(y + 2) + y = 6`
NOTE: The red symbolizes a `x`.

`1: 2y = 6 - 2`
`1: 2y = 4`
`1: y = 2`

Put the value of `y` into the first equation.
`x + y = 6`
`x + 2 = 6`
`x = 6 - 2`
`x = 4`

Conclusion: `x = 4` and `y=2`