Question

Eric traveled to two cities on a single highway. The total distance one way was 200 miles. The distance from his original location to the first city was 40 miles less than the distance from the first city to the second city. Suppose that x represents the distance from the original location to the first city and y represents the distance from the first city to the second city. The following system of equations represents the given situation. x + y = 200 x = y − 40 Which pair of coordinates represents the solution (in miles) to this system of equations? (70, 130) (80, 120) (160, 120) (100, 100) (140, 60)

Answer 1

Equation (1) x + y = 200

Eauation (2) x = y - 40

x represents the distance from the original location to the firstt city

y represents the distance from the first city to the second city.

Solution:

(1) x + y = 200

(2) x - y = - 40
----------------------

2x = 200 - 40

2x = 160

x = 160 / 2

x = 80

x + y = 200 => y = 200 - x = 200 - 80 = 120

Therefore the solution (x,y) is (80,120)

Answer: the pair of coordinates that represents the solution (in miles) to this system of equations is (80, 120)