#### Answer

$$x=2$$ $$y = 5$$

#### Work Step by Step

equation 1 $$3x + y = 11$$ equation 2 $$x + 2y = 12$$
Using equation 1, subtract $3x$ from both sides:
$$3x + y = 11$$ $$3x-3x + y = 11-3x$$ $$y = 11-3x$$
We will refer to $y = 11-3x$ as equation 1'.
Substituting this new equation 1 to equation 2:
$$x + 2y = 12$$ $$x + 2(11-3x) = 12$$ $$x + 22-6x = 12$$ $$22-5x = 12$$
Subtract $22$ from both sides:
$$22-22-5x = 12-22$$ $$-5x = -10$$ Divide both sides by $-5$: $$\frac{-5x}{-5} = \frac{-10}{-5}$$ $$x=2$$
Substitute this value to equation 1':
$$y = 11-3x$$ $$y = 11-3(2)$$ $$y = 11-6$$ $$y = 5$$