Final Answer:
The system of equations for the scenario is: x + y = 142, x - y = 14
Solving this system gives you: x = 78, y = 64
Therefore, the larger number is 78 and the smaller number is 64.
Step-by-step explanation:
Define the variables: Let x be the larger number and y be the smaller number.
Translate the information into equations:
The sum of x and y is 142, so write x + y = 142.
The difference between x and y is 14, so write x - y = 14.
Solve the system: You can solve this system using various methods like elimination or substitution. Here, we'll use elimination:
Add the two equations together:
2x = 156
Divide both sides by 2:
x = 78
Substitute this value for x in either of the original equations to find y:
78 - y = 14;
y = 64.
Therefore, the system of equations successfully represents the given scenario and allows you to find the individual values of x and y.
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Complete Question
The sum of two numbers, x and y, is 142. Their difference is 14. Write a system of equations for the scenario and solve.
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