Identify given equations

Note down the two simultaneous linear equations provided in the question.

$3x + 2y = 12, \quad 2x - y = 1$

Equalize coefficients

Multiply the second equation by 2 so the coefficient of $y$ becomes $-2$, matching the opposite of the coefficient in the first equation.

$4x - 2y = 2$

Add equations to eliminate y

Add the modified second equation to the first equation: $(3x + 4x) + (2y - 2y) = 12 + 2$.

$7x = 14$

Solve for x

Divide both sides by 7 to isolate $x$.

$x = \frac{14}{7} = 2$