#### Answer

$(\frac{1}{2}, \frac{1}{2})$

#### Work Step by Step

$x + y = 1$
$4x - 2y= 1$
When we multiply the first equation by 2, the system becomes
$2x + 2y = 2$
$4x - 2y = 1$
Adding these equations yields $6x = 3$, so $x = \frac{1}{2}$. Substituting $x = \frac{1}{2}$ into the first equation, we get $\frac{1}{2} + y = 1$. Then $y = \frac{1}{2}$. So the solution is $(\frac{1}{2}, \frac{1}{2})$.