word problem and a system of equation

Question

Mr. Sparks & Mr. Ben go out to buy pizza during lunch. Mr. Ben purchased 4 slices of pizza and 2 sodas for $14, and Mr. Sparks purchased 5 slices of pizza and 3 sodas for $18.25. Write and solve a system of equations to determine the price of one slice of pizza and one soda.

Answer 1

4P + 2S = 14

5P +3S = 18.25

multiply the 2nd equation by 2 and the 1st by 3, then subtract them

12P+6S = 42

10P +6S=36.5

2P = 5.5 divide by 2

P=5.5/2 = $2.75 for a slice of pizza

S= (14-4P)/2 = (14-11)/2 = $1.50 for a soda