Solving a System of Equations Using the Elimination Method

Math Problem Statement

Solve the system of equations: \(2x - 3y = 14\) and \(x + 3y = -11\).

The system of equations provided in the image is:

2x - 3y = 14 \\ x + 3y = -11 \end{cases}$$ To solve this system of equations, we can use the elimination method. Let's go through the solution step by step. ### Step 1: Add the Equations To eliminate $$y$$, we add the two equations together: $$(2x - 3y) + (x + 3y) = 14 + (-11)$$ This simplifies to: $$3x = 3$$ ### Step 2: Solve for $$x$$ Divide both sides by 3: $$x = 1$$ ### Step 3: Substitute $$x = 1$$ into the Second Equation Now, substitute $$x = 1$$ into the second equation to find $$y$$: $$1 + 3y = -11$$ Subtract 1 from both sides: $$3y = -12$$ Now, divide by 3: $$y = -4$$ ### Solution The solution to the system is: $$x = 1, \quad y = -4$$ Would you like further details on any steps or have questions about similar problems? Here are five related questions to expand on this topic: 1. How do you determine whether to use substitution or elimination for solving systems of equations? 2. What are the steps to solve a system of equations if both variables have the same coefficient in one equation? 3. How can we check if the solution we found is correct for both equations? 4. What are some real-world applications of solving systems of linear equations? 5. How would this system change if we were solving for three variables instead of two? **Tip:** When solving systems of equations, carefully check each step, especially when simplifying terms, to avoid small errors that can lead to incorrect solutions.

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Algebra
Systems of Equations
Elimination Method

Elimination method for solving systems of equations

Addition Property of Equality

Grades 8-10

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