A travel agency offers two Dallas outings. Plan A includes hotel accommodations for three nights and two pairs of Texas Rangers baseball tickets worth a total of $557. Plan B includes hotel accommodations for five nights and four pairs of Rangers baseball tickets worth $974. Find the cost of one night's hotel accommodations and the cost of one pair of baseball tickets.

We let x as the cost of one night’s hotel accommodations and y as the cost of one pair of baseball tickets. For plan A, we can generate the equation as 3x + 2y = $557 and for plan B; 6x + 4y = $1114

Using elimination, we can write the two as:

3x + 2y = 557

5x + 4y = 974

Multiply both eq. 1 by 2 to eliminate y

2 (3x + 2y = 557) 2

6x + 4y = 1114

We now have

6x + 4y = 1114

5x + 4y = 974 ⇒ subtract

X = 140

Substitute x to either equation to get the value of y

3 (140) + 2y = 557

2y = 557 - 420

2y = 137

Y = 68.5