Question

select the correct answer.

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)

Explanation:

Identify the system of equations

Using the Systems of Linear Equations knowledge point

$$
LATEXBLOCK0
$$

Substitute the second equation into the first

Using the Systems of Linear Equations knowledge point

$$
LATEXBLOCK1
$$

Solve for x

Using the Systems of Linear Equations knowledge point

$$
LATEXBLOCK2
$$

Write the solution as a coordinate pair

Using the Systems of Linear Equations knowledge point

$$ (x, y) = (80, 120) $$

Answer:

• (A) \((70, 130)\)
• (B) \((80, 120)\) (Correct answer)
• (C) \((160, 120)\)
• (D) \((100, 100)\)
• (E) \((140, 60)\)