Math Problem Statement
x-y=6 over 2x + y = 3
Solution
To solve the system of equations:
1.\ & x - y = 6 \\ 2.\ & 2x + y = 3 \end{aligned}$$ We can solve it using either substitution or elimination. I'll use the **substitution method**: ### Step 1: Solve the first equation for $$x$$: $$x = y + 6$$ ### Step 2: Substitute $$x = y + 6$$ into the second equation: $$2(y + 6) + y = 3$$ ### Step 3: Simplify and solve for $$y$$: $$2y + 12 + y = 3 \\ 3y + 12 = 3 \\ 3y = 3 - 12 \\ 3y = -9 \\ y = -3$$ ### Step 4: Substitute $$y = -3$$ back into the expression for $$x$$: $$x = -3 + 6 \\ x = 3$$ ### Final Answer: The solution to the system is: $$x = 3, \quad y = -3$$ Would you like more details or have any questions? Here are 5 related questions to expand your understanding: 1. How would you solve the system using the elimination method? 2. What happens if you graph both equations? Where do they intersect? 3. Can you express the solution as a vector? 4. What is the determinant of the coefficient matrix for this system? 5. How can you verify the solution? **Tip:** When solving systems of equations, always check your solution by substituting the values back into the original equations.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Systems of linear equations
Substitution method
Elimination method
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12