Question

Find the point of intersection for each pair of lines algebraically. $$y=-2 x-1 ; y=x+2$$

   Find the point of intersection for each pair of lines algebraically.
$$y=-2 x-1 ; y=x+2$$

Precalculus : Building Concepts and Connections

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 1, Problem 21

Instant Answer

Solved by Expert Xiaomeng Zhang

08/19/2020

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This gives us: \[-2x - 1 = x + 2\] Show more…

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Find the point of intersection for each pair of lines algebraically. $$y=-2 x-1 ; y=x+2$$

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Key Concepts

System of Linear Equations

A system of linear equations consists of multiple equations involving the same variables. Each equation represents a line or plane, and the solution to the system is the set of values that satisfy all the equations simultaneously. This is a fundamental concept in algebra and is used to find common solutions such as intersection points.

Intersection of Lines

The intersection of lines occurs where two or more lines cross each other on a coordinate plane. This point of intersection represents the common solution to the equations of the lines involved, meaning it satisfies each equation simultaneously.

Substitution Method

The substitution method is an algebraic technique used to solve systems of equations. It involves solving one of the equations for one variable and then substituting that expression into the other equation(s), which allows for the determination of the value of the remaining variable(s).

Algebraic Manipulation

Algebraic manipulation refers to the process of rearranging and simplifying equations using operations such as addition, subtraction, multiplication, division, and substitution. This process is essential for solving equations, including those in systems of linear equations, to isolate and determine the values of the variables.

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