Write down the given equations

We have two equations: Equation (1) is $4x + 3y = 18$ and Equation (2) is $2x - y = 4$.

$4x + 3y = 18, \quad 2x - y = 4$

Eliminate y by equating coefficients

Multiply Equation (2) by $3$ so that the coefficients of $y$ in both equations become opposites ($3y$ and $-3y$).

$3(2x - y) = 3(4) \implies 6x - 3y = 12$

Add the equations

Add the modified Equation (2) to Equation (1) to eliminate $y$: $(4x + 3y) + (6x - 3y) = 18 + 12$.

$10x = 30$

Solve for x

Divide both sides by $10$ to find the value of $x$: $x = \frac{30}{10}$.

$x = 3$