Let's call pizza p and soft drink s

5 p + 5 s = 21.75

5 (p+s) = 21.75

p+s = 21.75/5

p + s = 4.35

now we know that 1 slice of pizza and 1 drink costs $4.35

s = 4.35 - p

and

p = 4.35 -s

now to the other part of 7 slices of pizza and 6 soft drinks

7 p + 6 s = 29.16

lets solve for p the pizza

plug in 4.35 - p

7p + 6 (4.35 - p) = 29.96

7p + 26.10 - 6p = 29.96

7p-6p = 29.96 -26.10

p = 3.86

pizza = p = $3.86 per slice

let solve for s the soft drink

4.35 - p = s

4.35 - 3.86 = .49 for the soft drink

lets check

7p + 6s = 29.96

7 x 3.86 = 27.02

6 X .49 = 2.94

27.02 + 2.97 = 29.97

so really pizza would probably be 3.85 and the soft drink is .50

the numebrs came out strange due to rounding

5 p + 5 s = 21.75

5 (p+s) = 21.75

p+s = 21.75/5

p + s = 4.35

now we know that 1 slice of pizza and 1 drink costs $4.35

s = 4.35 - p

and

p = 4.35 -s

now to the other part of 7 slices of pizza and 6 soft drinks

7 p + 6 s = 29.16

lets solve for p the pizza

plug in 4.35 - p

7p + 6 (4.35 - p) = 29.96

7p + 26.10 - 6p = 29.96

7p-6p = 29.96 -26.10

p = 3.86

pizza = p = $3.86 per slice

let solve for s the soft drink

4.35 - p = s

4.35 - 3.86 = .49 for the soft drink

lets check

7p + 6s = 29.96

7 x 3.86 = 27.02

6 X .49 = 2.94

27.02 + 2.97 = 29.97

so really pizza would probably be 3.85 and the soft drink is .50

the numebrs came out strange due to rounding