Math Problem Statement
Solve the system of equations: 3x + 5y = -19 and x - 3y = 17
Solution
The system of equations provided in the image is:
3x + 5y = -19 \\ x - 3y = 17 \end{cases}$$ We can solve this system using either substitution or elimination. Let's use substitution: ### Step 1: Solve for $$x$$ from the second equation. From $$x - 3y = 17$$, we can solve for $$x$$ as: $$x = 17 + 3y$$ ### Step 2: Substitute $$x = 17 + 3y$$ into the first equation. Now, substitute this expression for $$x$$ into the first equation $$3x + 5y = -19$$: $$3(17 + 3y) + 5y = -19$$ Expanding the equation: $$51 + 9y + 5y = -19$$ Combine like terms: $$51 + 14y = -19$$ Solve for $$y$$: $$14y = -19 - 51$$ $$14y = -70$$ $$y = \frac{-70}{14} = -5$$ ### Step 3: Substitute $$y = -5$$ back into $$x = 17 + 3y$$. $$x = 17 + 3(-5) = 17 - 15 = 2$$ ### Solution: The solution to the system is: $$x = 2, \quad y = -5$$ Would you like further details or have any questions? Here are 5 related questions: 1. How do you check if the solution to a system of equations is correct? 2. What is the elimination method, and how does it compare to substitution? 3. Can a system of equations have more than one solution? Why or why not? 4. What are some applications of solving systems of equations in real life? 5. How can you solve a system of equations using matrix methods like Gaussian elimination? **Tip:** Always substitute your solution back into both original equations to verify its correctness.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
System of Linear Equations
Formulas
Substitution Method: Solve for one variable and substitute it into the other equation
Linear Equation Formula: ax + by = c
Theorems
Fundamental Theorem of Algebra
Suitable Grade Level
Grades 8-10