Math Problem Statement
Solve the system of equations: x + y = 5 and x - 2y = -1.
Solution
The system of equations provided in the image is:
x + y = 5 \\ x - 2y = -1 \end{cases}$$ Let's solve this system of linear equations using substitution or elimination. I will use the substitution method here. 1. From the first equation, solve for $$x$$: $$x = 5 - y$$ 2. Substitute $$x = 5 - y$$ into the second equation: $$(5 - y) - 2y = -1$$ 3. Simplify the equation: $$5 - y - 2y = -1 \quad \Rightarrow \quad 5 - 3y = -1$$ 4. Solve for $$y$$: $$-3y = -1 - 5 \quad \Rightarrow \quad -3y = -6 \quad \Rightarrow \quad y = 2$$ 5. Substitute $$y = 2$$ back into the equation $$x = 5 - y$$: $$x = 5 - 2 = 3$$ Thus, the solution to the system is $$x = 3$$ and $$y = 2$$. Would you like more details, or do you have any questions? Here are five related questions to expand on this topic: 1. How can you solve this system using the elimination method? 2. What happens if we graph these two equations on the coordinate plane? 3. Can you solve a similar system with three variables? 4. What is the general approach for solving nonlinear systems? 5. How do you check the solution of a system of equations? **Tip:** When solving systems of equations, always double-check your solution by substituting the values back into both original equations.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Systems of Equations
Formulas
Substitution Method
Elimination Method
Theorems
System of Equations Theorem
Suitable Grade Level
Grades 7-9