Solving System of Linear Equations: x - 2y = 1 and y

Math Problem Statement

Solve the system of equations: x - 2y = 1 and y - x = -2.

The system of linear equations given in the image is:

x - 2y = 1 \\ y - x = -2 \end{cases}$$ ### Step 1: Solve the second equation for $$y$$. The second equation is: $$y - x = -2$$ Add $$x$$ to both sides: $$y = x - 2$$ ### Step 2: Substitute $$y = x - 2$$ into the first equation. Substitute this into the first equation: $$x - 2(x - 2) = 1$$ Simplify: $$x - 2x + 4 = 1$$ $$-x + 4 = 1$$ Subtract 4 from both sides: $$-x = -3$$ Multiply both sides by $$-1$$: $$x = 3$$ ### Step 3: Substitute $$x = 3$$ back into the equation for $$y$$. Now substitute $$x = 3$$ into the equation $$y = x - 2$$: $$y = 3 - 2 = 1$$ ### Solution: The solution to the system of equations is: $$x = 3, \quad y = 1$$ Would you like more details on how to solve such systems, or do you have any questions? Here are 5 related questions you might explore: 1. How do you solve a system of equations by substitution? 2. What is the elimination method for solving systems of equations? 3. How can you represent a system of linear equations graphically? 4. Can systems of equations have no solution or infinitely many solutions? 5. How does solving systems of equations apply in real-world problems? **Tip**: When solving systems of equations, always simplify and substitute carefully to avoid errors.

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Algebra
Linear Equations
Systems of Equations

Substitution Method
Simplification of Linear Equations

Linear Substitution Theorem

Grades 8-10

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