Use elimination to solve system of equation
3x – 2y = 0
x + 6y = 5
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A riverboat on the Mississippi River travels 30 miles upstream in 2 hours and 30 minutes. The return trip downstream takes only 2 hours.
1. Find the rate of the current.
2. Find the rate of the riverboat in still water.
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The science club purchased tickets for a magic show. They paid $108 for 6 tickets in section A and 10 tickets in section B. The following week, they paid $104 for 4 tickets in section A and 12 tickets in section B.
1. Write a system of equations to represent the problem.
2. What are the prices of the tickets in section A and B?
Show work please.
Thanks
eq 1: 3x – 2y = 0
eq2: x + 6y = 5
in eq 2 subtract 6y from each side
x = 5 – 6y
substitute this into eq 1:
3(5- 6y) – 2y = 0
multiply out:
3*5 – 3*6y -2y = 0
15 – 18y -2y = 0
collect terms:
15 – 20y = 0
subtract 15 from both sides
-20y = -15y
divide both sides by -20
y = -15 / – 20
do arithmetic
y = 3/4 = 0.75
put this back into either of the equations and solve for x
eq 1: 3x – 2y = 0
eq2: x + 6y = 5
in eq 2 subtract 6y from each side
x = 5 – 6y
substitute this into eq 1:
3(5- 6y) – 2y = 0
multiply out:
3*5 – 3*6y -2y = 0
15 – 18y -2y = 0
collect terms:
15 – 20y = 0
subtract 15 from both sides
-20y = -15y
divide both sides by -20
y = -15 / – 20
do arithmetic
y = 3/4 = 0.75
put this back into either of the equations and solve for x
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