Solve the System of Equations: x + y = 3, x + 2y = -1 using Elimination

Math Problem Statement

Solve the system of equations: x + y = 3 and x + 2y = -1 using the elimination method.

The image contains a problem that asks to solve a system of equations using the elimination method:

1. & \quad x + y = 3 \\ 2. & \quad x + 2y = -1 \end{aligned}$$ ### Steps to solve by elimination: 1. **Subtract the first equation from the second** to eliminate $$x$$: $$(x + 2y) - (x + y) = -1 - 3$$ Simplifying: $$x - x + 2y - y = -4 \implies y = -4$$ 2. **Substitute** $$y = -4$$ into the first equation $$x + y = 3$$: $$x + (-4) = 3 \implies x = 3 + 4 = 7$$ Thus, the solution to the system is: $$x = 7, \quad y = -4$$ --- Do you want more details or have any questions? Here are some related questions: 1. What is the substitution method, and how does it differ from elimination? 2. How can we solve systems with no solutions or infinite solutions? 3. What are the conditions for a system to be consistent and independent? 4. Can elimination work for systems with more than two variables? 5. How does the graph of these two equations look, and where do they intersect? **Tip:** Always double-check your results by plugging the values back into the original equations to verify their correctness.

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Algebra
Linear Equations
System of Equations

Elimination method
Substitution method

Principle of Elimination

Grades 8-10

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