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

Nov 19, 2015

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.

$1 : \textcolor{red}{y + 2} + y = 6$
NOTE: The red symbolizes a $x$.

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

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

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