Question

Find the point of intersection for each pair of lines algebraically. $$-\frac{3}{2} x-y=3 ; x+y=-2$$

   Find the point of intersection for each pair of lines algebraically.
$$-\frac{3}{2} x-y=3 ; x+y=-2$$

Precalculus : Building Concepts and Connections

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 1, Problem 33

Instant Answer

Solved by Expert Xiaomeng Zhang

08/19/2020

Step 1

We can do this by adding the two equations together. This will eliminate the y variable. \[ -\frac{3}{2}x - y + x + y = 3 - 2 \] Show more…

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Find the point of intersection for each pair of lines algebraically. $$-\frac{3}{2} x-y=3 ; x+y=-2$$

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Key Concepts

Algebraic Methods for Solving Systems

Algebraic methods such as substitution and elimination are techniques used to solve systems of linear equations. Substitution involves solving one equation for one variable and then replacing that expression in the other equation, while elimination involves combining the equations in a way that cancels out one of the variables. These methods help to systematically determine the values of the variables that satisfy all equations in the system.

Intersection of Lines

The intersection point of lines represents the unique set of coordinates at which the lines cross each other. This point satisfies both linear equations simultaneously, meaning it is the solution to the system. The concept of intersection is essential in understanding the relationships between linear equations, such as whether the lines are parallel, coincident, or intersecting.

Systems of Linear Equations

A system of linear equations consists of two or more linear equations involving the same set of variables. The main goal is to find values for the variables that make all equations true at the same time. Geometrically, for two variables, each equation represents a line and the solution corresponds to the point where the lines intersect.

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