Math Problem Statement
Solve the system of equations:
-3 = -2A + 3B
2 = A + B
Solution
The system of equations given in the image is:
-3 = -2A + 3B \\ 2 = A + B \end{cases}$$ Let's solve this system step-by-step. ### Step 1: Solve the second equation for $$A$$ in terms of $$B$$. From $$2 = A + B$$: $$A = 2 - B$$ ### Step 2: Substitute $$A = 2 - B$$ into the first equation. Substituting into $$-3 = -2A + 3B$$: $$-3 = -2(2 - B) + 3B$$ Expanding and simplifying: $$-3 = -4 + 2B + 3B$$ $$-3 = -4 + 5B$$ $$5B = 1$$ $$B = \frac{1}{5}$$ ### Step 3: Substitute $$B = \frac{1}{5}$$ back into $$A = 2 - B$$. $$A = 2 - \frac{1}{5}$$ $$A = \frac{10}{5} - \frac{1}{5} = \frac{9}{5}$$ ### Solution The solution to the system is: $$A = \frac{9}{5}, \quad B = \frac{1}{5}$$ Would you like further details or have any questions? Here are some related questions for deeper understanding: 1. How can you verify the solution of a system of equations? 2. What methods can be used to solve a system of linear equations? 3. How does substitution work in systems with more than two variables? 4. What happens if a system of equations has no solution? 5. How can graphing help in solving systems of linear equations? **Tip:** When solving systems of equations, substitution is often useful when one of the equations is easily rearranged to isolate a variable.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Linear Equations
Formulas
Substitution method for solving systems of equations
Theorems
None
Suitable Grade Level
Grades 8-10