What are the steps to solving this equation? Thank you!

Question

Two families went to Rollercoaster World. The Brown family paid $170 for 3 children and 2 adults. The Peckham family paid $360 for 4 children and 6 adults. Determine the cost of a children’s ticket and an adult ticket.

Answer 1

3x + 2y = 170

4x + 6y = 360

Multiply the first equation by -3 to get:

-9x - 6y = --510

4x + 6y = 360

Add the equations to obtain -5x = -150

Solve for x and y.

Answer 2

3c +2a = 170

4c +6a =360

divide by 2

2c +3a = 360/2 = 180

multiply 1st equation by 2, 3rd by 3, to eliminate one variable

6c +9a = 540

6c + 4a = 2(170) = 340

9a-4a = 540-340

5a = 200

a = 200/5 = 40 adults

3c= 170 -2a

c = (170-2(40))/3= 90/3 = 30 children

4(30) +6(40) = 120+240 = 360

3(30) +2(40) = 90+80 = 170