Here are the essential concepts you must grasp in order to answer the question correctly.
Systems of Equations
A system of equations consists of two or more equations with the same variables. To solve such a system, one can use methods like substitution or elimination to find the values of the variables that satisfy all equations simultaneously. In this problem, we can set up two equations based on the given conditions about the sum and difference of the two numbers.
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Linear Equations
Linear equations are mathematical statements that describe a straight line when graphed. They typically take the form y = mx + b, where m is the slope and b is the y-intercept. In this problem, the relationships between the two numbers can be expressed as linear equations, allowing us to find their specific values.
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Algebraic Manipulation
Algebraic manipulation involves rearranging and simplifying equations to isolate variables and solve for unknowns. This includes operations such as adding, subtracting, multiplying, and dividing both sides of an equation. In this question, manipulating the equations derived from the sum and difference will lead to the solution for the two numbers.
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