Solve the following system of linear equations for a and b: 2a − b = 3 and a + b = 9

We have the following system:

$$2a - b = 3 \quad (1)$$ $$a + b = 9 \quad (2)$$

$$(2a - b) + (a + b) = 3 + 9$$ $$2a + a - b + b = 12$$ $$3a = 12$$

Divide both sides by 3:

$$\frac{3a}{3} = \frac{12}{3}$$ $$a = 4$$

$$a + b = 9$$

Substitute $a = 4$:

$$4 + b = 9$$

Subtract 4 from both sides:

$$b = 9 - 4$$ $$b = 5$$

The solution to the system of equations is:

$$a = \boxed{4}$$ $$b = \boxed{5}$$