Math Problem Statement
Solution
To solve for the value of , we can first solve the system of equations:
x + y &= 25 \quad \text{(Equation 1)} \\ x - y &= 5 \quad \text{(Equation 2)} \end{aligned}$$ ### Step 1: Add the two equations By adding Equation 1 and Equation 2, we eliminate $$y$$: $$(x + y) + (x - y) = 25 + 5$$ This simplifies to: $$2x = 30$$ ### Step 2: Solve for $$x$$ Divide both sides by 2: $$x = 15$$ ### Step 3: Find $$\frac{x}{3}$$ Now that we have $$x = 15$$, we calculate: $$\frac{x}{3} = \frac{15}{3} = 5$$ Thus, the value of $$\frac{x}{3}$$ is **5**. Would you like more details on this solution, or do you have any other questions? Here are 5 related questions you might find interesting: 1. What is the value of $$y$$ in the system of equations? 2. How would you solve this system of equations using substitution? 3. What happens if the equations are modified to $$x + y = 30$$ and $$x - y = 10$$? 4. How can these equations be solved using a graphical method? 5. How would the solution change if we were asked to find $$\frac{y}{3}$$ instead of $$\frac{x}{3}$$? **Tip:** When solving systems of linear equations, adding or subtracting the equations is a quick method to eliminate one of the variables.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Equations
System of Equations
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9