Solve by using system of equations. with 31, 32, and !

(31)

let x and y be the 2 numbers, x > y, then

x + y = 12 and

x - y = 4

add the 2 equations term by term

2x = 16 ( divide both sides by 2 )

x = 8

substitute x = 8 into x + y = 12

8 + y = 12 ⇔ y = 12 - 8 = 4

the 2 numbers are 8 and 4

(32)

let the 2 numbers be x and y, x > y, then

x - y = 3 and

x + y = 13

add the 2 equations term by term

2x = 16 ( divide both sides by 2 )

x = 8

substitute x = 8 into x + y = 13

8 + y = 13 ⇒ y = 13 - 8 = 5

the 2 numbers are 8 and 5

(33)

let s be the cost of senior citizen ticket and c be the cost of a child ticket, then

3s + c = 38 → (1)

3s + 2c = 52 → (2)

subtract (1) from (2) term by term

c = 14

substitute c = 14 into (1)

3s + 14 = 38 ( subtract 14 from both sides )

3s = 24 ( divide both sides by 3 )

s = 8

the cost of a senior citizen ticket is $8 and a child ticket is $14

step-by-step explanation: 2

c. 1,233 miles