Solving a System of Equations with Sum and Difference

Math Problem Statement

i am thinking of two numbers that dd up to 5 the difference between them is 9 what are the two numbers

Let's solve this step-by-step.

Let the two numbers be $x$ and $y$ . According to the problem:

We now have a system of two equations:

x + y &= 5 \\ x - y &= 9 \end{aligned}$$ ### Solving the system of equations: 1. Add the two equations together: $$(x + y) + (x - y) = 5 + 9$$ This simplifies to: $$2x = 14$$ 2. Solve for $$x$$: $$x = \frac{14}{2} = 7$$ 3. Substitute $$x = 7$$ into the first equation: $$7 + y = 5$$ 4. Solve for $$y$$: $$y = 5 - 7 = -2$$ ### Therefore, the two numbers are **7** and **-2**. Would you like further details or have any questions on this process? Here are some additional related questions you could explore: 1. How can we solve systems of equations using substitution? 2. What happens if the sum or difference changes in this kind of problem? 3. Can you solve a similar problem where the sum is a different value, say 10, and the difference is still 9? 4. How do we solve word problems like this one using algebraic methods? 5. What is the graphical representation of this system of equations? **Tip**: When solving a system of two linear equations, you can use either substitution or elimination. Choose the method that makes the equations easier to work with!

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Algebra
Systems of Linear Equations

x + y = 5
x - y = 9

Solving systems of linear equations using addition/subtraction method

Grades 7-9

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