Solving System of Linear Equations by Elimination Method

Math Problem Statement

Solve the system of equations using the method of elimination: 1. x - y = -1 2. -2x + 3y = -5

We are tasked with solving the system of equations using the method of elimination. The system is:

1. \ \ x - y &= -1 \\ 2. \ \ -2x + 3y &= -5 \end{aligned}$$ ### Step 1: Eliminate one variable We can eliminate the variable $$x$$ by multiplying the first equation by 2, so the coefficients of $$x$$ in both equations are opposites: $$2(x - y) = 2(-1) \quad \Rightarrow \quad 2x - 2y = -2$$ Now, we have the system: $$\begin{aligned} 2x - 2y &= -2 \\ -2x + 3y &= -5 \end{aligned}$$ ### Step 2: Add the equations Add the two equations to eliminate $$x$$: $$(2x - 2y) + (-2x + 3y) = -2 + (-5)$$ Simplifying: $$0x + y = -7$$ So, we get: $$y = -7$$ ### Step 3: Substitute the value of $$y$$ Now that we have $$y = -7$$, substitute this into the first original equation to find $$x$$: $$x - (-7) = -1 \quad \Rightarrow \quad x + 7 = -1$$ Solving for $$x$$: $$x = -1 - 7 = -8$$ ### Solution: The solution to the system is: $$x = -8, \quad y = -7$$ Would you like more details or have any questions? Here are 5 related questions you might want to consider: 1. How do you solve systems of equations by substitution instead of elimination? 2. Can elimination always be used to solve any system of linear equations? 3. What is the difference between consistent and inconsistent systems? 4. How do you solve a system of equations with three variables using elimination? 5. Can elimination be applied to non-linear systems of equations? **Tip:** Always check your solution by substituting both values back into the original equations to ensure accuracy.

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Algebra
Systems of Linear Equations
Method of Elimination

Linear equation: ax + by = c
Elimination method involves adding or subtracting equations to eliminate one variable

Elimination method for solving systems of equations

Grades 8-10

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