Solve the system of linear equations: 2x − y = 6 and x − y = 1.

$$2x - y = 6 \quad (1)$$ $$x - y = 1 \quad (2)$$

From equation (2), it's easiest to solve for $x$:

$$x - y = 1$$ $$x = 1 + y \quad (3)$$

Substitute equation (3) into equation (1):

$$2(1 + y) - y = 6$$

$$2 + 2y - y = 6$$ $$2 + y = 6$$ $$y = 6 - 2$$ $$y = 4$$

$$x = 1 + y$$ $$x = 1 + 4$$ $$x = 5$$

The solution is $x=5$ and $y=4$.

The solution to the system of equations is $x=5, y=4$.