Cost of each barbecue: x

Cost of each softdrink: y

Group A (Equation A):

10x + 12y = 320

Group B (Equation B):

6x + 4y = 160

Solve the system using Substitution Method:

Equation B:

6x + 4y = 160

4y = 160 - 6x

4y/4 = 160/4 - 6x/4

y = -3x/2 + 40

Substitute -3x/2 + 40 for y in Equation A:

10x + 12 (-3x/2 + 40) = 320

10x -18x + 480 = 320

-8x = 320 - 480

-8x/-8 = -160/-8

** x = 20**

Substitute 20 for x in y = -3x/2 + 40

y = -3(20)/2 + 40

y = -60/2 + 40

y = -30 + 40

**y = 10**

**Cost of each barbecue**: x = **Php 20**

**Cost of each softdrink**: y = **Php 10**

** ANSWER: A single barbecue costs Php20.**

Check:

Group A (Equation A):

10x + 12y = 320

10 (20) + 12 (10) = 320

200 + 120 = 320

320 = 320 (True)

Group B (Equation B):

6x + 4y = 160

6 (20) + 4 (10) = 160

120 + 40 = 160

160 = 160 (True)