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

Explanation:

x represents the distance from original location to the first city

y the distance from first to second city

x+y =200 and x=y-40

Let us write this in standard form

x+y =200 ... i

x-y =40 ... ii

We can solve this by elimination

Adding i and ii

we get

2x =240 or x =120

Substitute this in i

y = 200-120 =80

Hence solution is

(120,80)

The answer choice is given reverse as (80,120)

Answer 2

The equations are:
x + y = 200
x = y - 40; substituting x from this equation to the first:
y - 40 + y = 200
2y = 240
y = 120

Corresponding value of x:
x = 120 - 40
x = 80

The solution to this system is (80, 120)