Math Problem Statement
Solve the system of equations x+y = 5 and x−y = 1. What are the values of x and y?
Solution
To solve the system of equations:
1) & \quad x + y = 5 \\ 2) & \quad x - y = 1 \end{aligned}$$ We can use the method of addition (also known as elimination) to find the values of $$x$$ and $$y$$. ### Step 1: Add the two equations By adding the two equations, we can eliminate $$y$$: $$(x + y) + (x - y) = 5 + 1$$ This simplifies to: $$2x = 6$$ ### Step 2: Solve for $$x$$ Now, divide both sides by 2: $$x = \frac{6}{2} = 3$$ ### Step 3: Substitute $$x$$ back into one of the original equations We'll substitute $$x = 3$$ into the first equation $$x + y = 5$$: $$3 + y = 5$$ ### Step 4: Solve for $$y$$ Subtract 3 from both sides: $$y = 5 - 3 = 2$$ ### Final Answer: The values of $$x$$ and $$y$$ are: $$x = 3, \quad y = 2$$ Would you like further details or have any questions? Here are some related questions: 1. How would you solve the system $$2x + y = 7$$ and $$x - y = 4$$? 2. What is the substitution method for solving systems of equations? 3. How can you solve a system of equations using matrices? 4. Can you explain the graphical interpretation of solving a system of linear equations? 5. What happens if a system of equations has no solution? **Tip:** When solving systems of equations, always check your solution by substituting the values back into both original equations.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Systems of Linear Equations
Method of Addition (Elimination)
Substitution Method
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9