Question

Find the intersection of the two lines. $$2 x-y=6, x+2 y=8$$

   Find the intersection of the two lines.
$$2 x-y=6, x+2 y=8$$

Precalculus : Building Concepts and Connections

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 8, Problem 5

Instant Answer

Solved by Expert Vipender Yadav

04/16/2020

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Step 1: First, we have the two equations: $$2x - y = 6 \tag{1}$$ $$x + 2y = 8 \tag{2}$$ Show more…

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Find the intersection of the two lines. $$2 x-y=6, x+2 y=8$$

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Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations involving the same set of variables. The goal is to find values for the variables that satisfy all equations simultaneously, which is a fundamental concept in algebra and has applications in various areas of mathematics and science.

Intersection of Lines

The intersection of lines refers to the point where two or more lines meet when graphed in a coordinate plane. In the context of a system of linear equations, the intersection point represents the common solution to the equations, meaning it is the set of variable values that makes all the equations true.

Solving Methods

To find the solution to a system of linear equations, methods such as substitution or elimination can be used. These techniques help isolate variables and reduce the system step by step, allowing for the determination of the intersection point where the lines cross.

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