Solve the system using any method.
x + y = 4.4
2x + y = 3.8
What is the solution of the system of equations?
(Simplify your answer. Type an ordered pair. Type an integer or a decimal.)
The solution to the system of equations is (-0.6, 5).
verage movie prices in the United States are, in general, lower than in other countries. It would cost $78.09 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $73.96. How much does an average movie ticket cost in each of these countries?
In Japan the average cost is $ [ ].
In Switzerland the average cost is $ [ ].
Let's assume the cost of a movie ticket in Japan is x dollars and the cost of a movie ticket in Switzerland is y dollars.
According to the given information:
3x + 2y = 78.09 (Equation 1)
2x + 3y = 73.96 (Equation 2)
We can solve this system of equations using any method, such as substitution or elimination.
Let's solve using the substitution method:
From Equation 1, we can express y in terms of x:
y = (78.09 - 3x)/2
Substitute this value of y in Equation 2:
2x + 3((78.09 - 3x)/2) = 73.96
2x + (234.27 - 9x)/2 = 73.96
Multiplying through by 2 to clear the fraction:
4x + 234.27 - 9x = 147.92
-5x = -86.35
Dividing by -5 on both sides:
x = 17.27
Substitute this value of x in Equation 1 to find y:
3(17.27) + 2y = 78.09
51.81 + 2y = 78.09
2y = 26.28
y = 13.14
Therefore, the average cost of a movie ticket in Japan is $17.27 and in Switzerland is $13.14.