Math Problem Statement
Solution
The problem states:
- The sum of two numbers is 90.
- Their difference is 12.
- We are asked to find the two numbers.
Let the two numbers be represented by and .
We have the following system of equations:
- (the sum of the two numbers)
- (the difference of the two numbers)
Now, we can solve this system of equations using the addition method. By adding both equations:
Simplifying:
Solving for :
Now substitute into the first equation :
Solving for :
Thus, the two numbers are and .
Would you like further details on how I solved this? Or do you have another question?
Here are some related questions you can explore:
- How do you solve systems of linear equations by substitution?
- What are some real-world applications of systems of equations?
- How do you graph the solutions to a system of linear equations?
- How can we solve a system of equations if one equation involves multiplication?
- How do you check the solution to a system of equations?
Tip: When solving systems of equations, always check your solutions by substituting them back into the original equations to verify they satisfy both equations.
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Linear Equations
Formulas
x + y = 90
x - y = 12
Theorems
Addition and Substitution Methods
Suitable Grade Level
Grades 6-8
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