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The system of equations has one solution, which is the ordered pair \((4, 1)\).

Would you like further clarification or details? Here are some follow-up questions to deepen your understanding:

1. How do you determine the number of solutions for a system of equations?
2. What methods can be used to solve a system of linear equations, such as substitution or elimination?
3. Can a system of linear equations have no solution or infinitely many solutions? Under what conditions?
4. How would the graph of this system of equations look like?
5. What are the benefits of using algebraic methods over graphical methods when solving systems of equations?

**Tip:** When dealing with systems of equations, checking the determinant of the coefficients matrix helps identify if the system has a unique solution, no solution, or infinitely many solutions.

Solve the system of equations: 6x - 5y = 19 and 7x + 3y = 31.

Learn how to solve the system of linear equations 6x - 5y = 19 and 7x + 3y = 31 using algebraic methods such as substitution or elimination. This problem focuses on key concepts like solving systems of equations and determining the number of solutions, suitable for students in Grades 8-10.

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