Math Problem Statement
A student states the solution to the system of equations \(-4x + 6y = 32\) and \(3x + y = 20\) is \((4, 8)\). Check if the solution \((4, 8)\) is correct by substituting the values into both equations.
Solution
To verify the solution for the system of equations:
-4x + 6y &= 32 \\ 3x + y &= 20 \end{aligned}$$ Substitute $$x = 4$$ and $$y = 8$$ into both equations. ### First equation: $$-4(4) + 6(8) = -16 + 48 = 32$$ This matches the left-hand side of the equation, so it is correct for the first equation. ### Second equation: $$3(4) + 1(8) = 12 + 8 = 20$$ This also matches the left-hand side of the second equation, so it is correct for the second equation. Thus, the solution $$(4, 8)$$ satisfies both equations, and the solution is **correct**. Would you like further clarification or a more detailed explanation? Here are some related questions for you to explore: 1. How can you solve this system of equations using substitution? 2. What method can be used to solve this system of equations besides substitution? 3. How do you determine if a solution is valid for a system of linear equations? 4. What happens if you substitute incorrect values into the equations? 5. Can you solve this system of equations graphically? **Tip:** Always check the solution by substituting back into both equations to ensure accuracy before concluding that it's correct.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Systems of Linear Equations
Substitution Method
Verification of Solutions
Formulas
General form of a linear equation: ax + by = c
Theorems
Properties of Equality
Suitable Grade Level
Grades 8-10
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