Math Problem Statement
Solve the system by the addition method: 3x + 8y = 3 and 4x - 8y = 4.
Solution
Let's solve the system of equations using the addition method (also known as the elimination method). The system of equations is:
3x + 8y &= 3 \\ 4x - 8y &= 4 \end{aligned}$$ ### Step 1: Add the two equations together. Since the coefficients of $$y$$ are opposites ($$8y$$ and $$-8y$$), adding the two equations will eliminate $$y$$. $$(3x + 8y) + (4x - 8y) = 3 + 4$$ Simplifying: $$3x + 4x + 8y - 8y = 7$$ $$7x = 7$$ ### Step 2: Solve for $$x$$. $$x = \frac{7}{7} = 1$$ ### Step 3: Substitute $$x = 1$$ back into one of the original equations to solve for $$y$$. Let's use the first equation: $$3(1) + 8y = 3$$ Simplifying: $$3 + 8y = 3$$ $$8y = 3 - 3$$ $$8y = 0$$ $$y = \frac{0}{8} = 0$$ ### Final Solution: The solution to the system is $$x = 1$$ and $$y = 0$$, or as an ordered pair, $$(1, 0)$$. ### Answer: The correct choice is **A. The solution set is $$(1, 0)$$**. Would you like further details on any of the steps? Here are 5 related questions you might find useful: 1. What is the elimination (addition) method and when is it used? 2. How can we solve the system using the substitution method instead? 3. What happens if there are no opposites to eliminate a variable in a system? 4. Can you explain how systems with no solution or infinitely many solutions look like graphically? 5. How can we check if our solution is correct by substitution? **Tip:** Always check your solution by substituting both $$x$$ and $$y$$ back into the original equations.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Linear Equations
Addition Method
Formulas
Addition of two linear equations: ax + by = c
Solving for a variable: x = c/a
Theorems
Linear Combination in Systems of Equations
Suitable Grade Level
Grades 9-10
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