Math Problem Statement
Solve the system of equations: 2x + y = 10, -2y = -24 + 4x
Solution
To solve the system of equations:
1. & \quad 2x + y = 10 \\ 2. & \quad -2y = -24 + 4x \end{aligned}$$ ### Step 1: Simplify the second equation Rearrange the second equation: $$-2y = 4x - 24$$ Divide through by $$-2$$: $$y = -2x + 12$$ ### Step 2: Substitute $$y = -2x + 12$$ into the first equation Substitute into $$2x + y = 10$$: $$2x + (-2x + 12) = 10$$ Simplify: $$2x - 2x + 12 = 10$$ $$12 = 10$$ ### Step 3: Analyze the results The statement $$12 = 10$$ is **false**. This means the system of equations has **no solution**. ### Final Answer: The correct choice is: **No solution**. Let me know if you'd like further explanation or a breakdown of the concepts! --- Here are 5 questions you can consider next: 1. What does it mean graphically when a system of equations has no solution? 2. How can you verify the solution of a system algebraically? 3. What is the difference between consistent and inconsistent systems of equations? 4. Can elimination or substitution methods yield a different result here? 5. How does solving a linear system relate to solving real-world problems? **Tip:** When simplifying systems of equations, always check for contradictions (e.g., statements like $$12 = 10$$) to identify inconsistency.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Linear Equations
Substitution Method
Formulas
y = mx + b
ax + by = c
Theorems
Linear systems
Contradiction in systems of equations
Suitable Grade Level
Grades 8-10