Math Problem Statement
Solve the system by the substitution method: x + y = -6, y = -3x. Select the correct choice from A, B, or C.
Solution
We are given the system of equations:
x + y &= -6 \\ y &= -3x \end{aligned}$$ To solve this system by the substitution method, follow these steps: ### Step 1: Substitute the second equation into the first Since $$y = -3x$$, substitute this expression for $$y$$ in the first equation: $$x + (-3x) = -6$$ Simplifying: $$x - 3x = -6 \implies -2x = -6$$ ### Step 2: Solve for $$x$$ Divide both sides of the equation by $$-2$$: $$x = \frac{-6}{-2} = 3$$ ### Step 3: Substitute $$x = 3$$ back into the equation for $$y$$ Using the second equation $$y = -3x$$: $$y = -3(3) = -9$$ ### Step 4: Solution as an ordered pair The solution to the system is $$(x, y) = (3, -9)$$. ### Final Answer: The solution set is $$(3, -9)$$, which corresponds to option **A**. Would you like further clarification on any step? Here are 5 related questions for more practice: 1. How would you solve the same system using the elimination method? 2. What would the solution look like if the equations represented parallel lines? 3. How do you recognize if a system of equations has no solution or infinite solutions? 4. Can substitution always be used to solve any system of linear equations? 5. How does graphing help visualize the solution to a system of equations? **Tip:** When solving systems by substitution, always simplify one equation first if possible, to make substitution easier.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Systems
Substitution Method
Formulas
Substitute y = -3x into x + y = -6
Simplified Equation: x - 3x = -6
Theorems
Solution of linear systems
Suitable Grade Level
Grades 8-10