Acompany makes 3 types of cable. cable a requires 3 black, 3 white, and 2 red wires. b requires 1 black, 2 white, and 1 red wire. c requires 2 black, 1 white, and 2 red wire. they used 120 black, 110 white and 100 red wires. how many of each cable were made? setup the system of equations to solve this problem by selecting the coefficients and constants for each colored wires.

Let
x =  the number of a-cables
y = the number of b-cables
z =  the number of c-cables

Cable a uses 3 black, 3 white and 2  red wires.
Cable b uses 1 black, 2 white and 1 red wire.
Cable c uses 2 black, 1 white and 2  red wires.

Because 120 black, 110 white and 100 red wires were used, therefore the system of equations is
3x +   y + 2z = 120        (1)
3x + 2y +   z = 110         (2)
2x +   y + 2z = 100        (3)

 
3x +  y + 2z = 120
3x + 2y  + z = 110
2x  + y + 2z = 100

where
x,y,z = the number of a, b and c-cables respectively.