Math Problem Statement
Find the solution to the system of equations: 2x + 3y = 1, 3x - 2y = 11.
Solution
The image you uploaded contains a system of equations that need to be solved. Here's the system of equations from the image:
2x + 3y &= 1, \\ 3x - 2y &= 11. \end{aligned}$$ ### Solving the System We can solve this system using either substitution or elimination. I'll use the elimination method. 1. **Multiply the equations to eliminate one variable:** - Multiply the first equation by 2: $$4x + 6y = 2$$ - Multiply the second equation by 3: $$9x - 6y = 33$$ 2. **Add the two equations to eliminate $$y$$:** $$(4x + 6y) + (9x - 6y) = 2 + 33$$ $$13x = 35$$ $$x = \frac{35}{13}$$ 3. **Substitute $$x$$ back into one of the original equations to solve for $$y$$:** $$2\left(\frac{35}{13}\right) + 3y = 1$$ $$\frac{70}{13} + 3y = 1$$ $$3y = 1 - \frac{70}{13} = \frac{13}{13} - \frac{70}{13} = \frac{-57}{13}$$ $$y = \frac{-57}{39} = \frac{-19}{13}$$ ### Solution So, the solution to the system is: $$x = \frac{35}{13}, \quad y = \frac{-19}{13}$$ If you enter your answer in the form $$x, y$$, it should be: $$\left(\frac{35}{13}, \frac{-19}{13}\right)$$ Would you like more details or have any questions about this solution? Here are some related questions: 1. How would you solve the system using the substitution method? 2. What would the solution be if you used matrix methods (e.g., Gaussian elimination)? 3. How do you interpret the solution of a system of equations graphically? 4. Could you explain what happens if a system of equations has no solution or infinitely many solutions? 5. What are some real-world applications of solving systems of equations? **Tip:** When solving systems of equations, always double-check your work by substituting your solution back into the original equations to ensure they satisfy both equations.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
System of Equations
Formulas
Elimination method
Substitution method
Theorems
System of linear equations
Suitable Grade Level
Grades 9-12
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