Math Problem Statement
Show work
Solve the system of linear equations: 3x - y = 7 and 3x - y = 7.
Solution
The image contains a system of linear equations:
3x - y = 7 \\ 3x - y = 7 \end{cases}$$ It seems both equations are identical, which indicates that there is an infinite number of solutions, as they represent the same line in the coordinate plane. Essentially, the system is dependent, and any solution that satisfies one equation will also satisfy the other. To understand this further, let's explore the steps: 1. **Solving for one variable**: You can solve for $$y$$ or $$x$$ by isolating one of the variables. Let's isolate $$y$$ in the first equation. $$3x - y = 7$$ $$y = 3x - 7$$ 2. **Interpretation of the system**: Since both equations are exactly the same, we can conclude that there isn't a unique solution. Instead, there are infinitely many solutions along the line $$y = 3x - 7$$. --- If you want to explore this further, here are some questions to consider: 1. How would you solve a system of two linear equations with different slopes? 2. What is the graphical interpretation of a system of linear equations with infinite solutions? 3. How can you solve a system of equations where one is a multiple of the other? 4. What is the difference between dependent and independent systems of equations? 5. How do you check if two equations are equivalent? **Tip**: When working with linear systems, always check for duplicate equations or multiples of each other, as this could indicate infinite solutions.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Equations
System of Equations
Dependent Systems
Formulas
3x - y = 7
Theorems
Solution of a system of linear equations
Suitable Grade Level
Grades 7-9