Solving Systems of Equations Using Substitution: y = x

Math Problem Statement

Solve each system by substitution.

Solve each system by substitution. y = x - 2 and y = 4x + 1.

We are given a system of two linear equations:

y = x - 2 \\ y = 4x + 1 \end{cases}$$ ### Step 1: Set the two equations equal to each other Since both equations are already solved for $$y$$, we can set them equal to each other: $$x - 2 = 4x + 1$$ ### Step 2: Solve for $$x$$ Now, solve the equation for $$x$$: 1. Subtract $$x$$ from both sides: $$-2 = 3x + 1$$ 2. Subtract 1 from both sides: $$-3 = 3x$$ 3. Divide both sides by 3: $$x = -1$$ ### Step 3: Substitute $$x = -1$$ back into one of the original equations Substitute $$x = -1$$ into either equation. Let's use the first equation: $$y = x - 2$$ $$y = -1 - 2 = -3$$ ### Final Solution: The solution to the system is $$x = -1$$ and $$y = -3$$. Therefore, the solution is: $$(x, y) = (-1, -3)$$ Would you like more details, or do you have any questions? Here are 5 related questions: 1. How do you solve a system of equations using the elimination method? 2. What happens if a system of equations has no solution? 3. How can you graphically interpret the solution to this system? 4. How do you solve a system of non-linear equations by substitution? 5. How do systems of equations relate to real-world problems? **Tip:** In substitution, always solve for one variable first and substitute it into the other equation for a systematic approach.

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Algebra
Systems of Linear Equations
Substitution Method

y = mx + b
Equation solving via substitution

Properties of Equality

Grades 8-10

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