How do I turn this into a system of equations?

During a 4th of july weekend 32 vehicles became trapped on sunshine bridge while it was being repaved. A recent city ordinance decreed that only cars with only 4 wheels and trucks with 6 wheels could be on the bridge at a time. If there were 148 tires that needed to be replaced due to damage, how many cars and trucks would be involved in the accident?

x = cars

y = trucks

$\begin{array}{lrcll} (1)& x + y &=& 32 \\ & x &=& 32 - y \\\\ (2) &4x+6y &=& 148 \\ &4\cdot (32-y) +6y &=& 148 \\ & 4\cdot 32 -4y + 6y &=& 148 \\ & 4\cdot 32 + 2y &=& 148 \quad & | \quad : 2\\ & 2\cdot 32 + y &=& 74\\ & 64 + y &=& 74 \quad & | \quad -64\\ & y &=& 74 -64\\ & \mathbf{ y }& \mathbf{=} & \mathbf{ 10 }\\\\ & x &=& 32 - y \\ & x &=& 32 - 10 \\ & \mathbf{ x }& \mathbf{=} & \mathbf{ 22 } \end{array}$

22 cars and 10 trucks

Call the number of cars = x  ...  and the number of wheels on the cars  = 4x

Call the number of trucks (32 - x)  ....  and the number of wheels on the trucks = (32 - x)6

So we have

4x + (32 - x)6  = 148    simplify

4x + 192 - 6x  = 148

-2x + 192  = 148     subtract 192 from each side

-2x  = -44     divide both sides by -2

x = 22  cars        and   (32 - x)  =   (32 - 22)   = 10 trucks