Math Problem Statement
x + y = 5 and -x+2y=4
Solution
To solve the system of equations:
1. & \quad x + y = 5 \quad \text{(Equation 1)} \\ 2. & \quad -x + 2y = 4 \quad \text{(Equation 2)} \end{aligned}$$ We can use either the substitution method or the elimination method. Here, I'll use the elimination method. ### Step 1: Add the two equations First, we add Equation 1 and Equation 2 to eliminate $$x$$: $$(x + y) + (-x + 2y) = 5 + 4$$ This simplifies to: $$y + 2y = 9$$ $$3y = 9$$ ### Step 2: Solve for $$y$$ Now, solve for $$y$$: $$y = \frac{9}{3} = 3$$ ### Step 3: Substitute $$y = 3$$ back into one of the original equations Use Equation 1 to find $$x$$: $$x + y = 5$$ $$x + 3 = 5$$ $$x = 5 - 3 = 2$$ ### Final Solution The solution to the system of equations is: $$x = 2, \quad y = 3$$ Would you like to go over any details or have any further questions? --- Here are some related questions you might find interesting: 1. What happens if we multiply Equation 1 by a constant before using the elimination method? 2. How would you solve this system using the substitution method instead? 3. Can you graphically represent the solution to these equations? 4. What would the solution be if one of the equations were non-linear? 5. How would this problem change if you had three variables instead of two? **Tip:** When solving systems of equations, it's useful to double-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
Elimination Method
Substitution Method
Formulas
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Theorems
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Suitable Grade Level
Grades 8-10