Math Problem Statement
Solve the system of equations:
1. x1 + 4x3 + 3x4 = 26
2. x2 - 3x3 - 3x4 = -26
3. 2x1 - 2x2 + 10x3 + 12x4 = 76
4. -x2 + 3x3 + 9x4 = 26
Solution
Let's analyze and solve the system of equations from the image.
The system is:
x_1 + 4x_3 + 3x_4 = 26 \\ x_2 - 3x_3 - 3x_4 = -26 \\ 2x_1 - 2x_2 + 10x_3 + 12x_4 = 76 \\ -x_2 + 3x_3 + 9x_4 = 26 \end{cases}$$ We will solve this system step by step. ### 1. Equation 1: $$x_1 + 4x_3 + 3x_4 = 26$$ ### 2. Equation 2: $$x_2 - 3x_3 - 3x_4 = -26$$ ### 3. Equation 3: $$2x_1 - 2x_2 + 10x_3 + 12x_4 = 76$$ ### 4. Equation 4: $$-x_2 + 3x_3 + 9x_4 = 26$$ Now, let's solve this system for $$x_1, x_2, x_3, x_4$$. I will begin by applying methods like substitution or elimination. Let me calculate this.The correct solution to the system of equations is: $$x_1 = -2, \quad x_2 = -5, \quad x_3 = 7, \quad x_4 = 0$$ It seems the provided answers $$x_2 = 13$$, $$x_3 = 1$$, and $$x_4 = 8$$ are incorrect. Would you like further details or clarifications? Here are some related questions for you: 1. How can you verify the solution of a system of equations? 2. What is the method of substitution, and how does it apply to solving systems? 3. How does the elimination method work for solving systems of linear equations? 4. What are the advantages of using matrix methods (e.g., Gaussian elimination) for larger systems? 5. Can systems of equations have no solution, and how do you identify such cases? **Tip:** Always substitute your solution back into the original system to verify correctness.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Systems of Linear Equations
Formulas
Substitution Method
Elimination Method
Theorems
Basic principles of solving systems of linear equations
Suitable Grade Level
Grades 10-12