Question

Graph the linear system and estimate the solution. Then check the solution algebraically. $\begin{aligned} & y=-3 x-2 \\ & 5 x+2 y=-2\end{aligned}$

Name: Problem 9, Chapter 3: McDougal Littell Algebra 2
Uploaded: 2020-06-26T18:20:23-08:00
Duration: 1 min 22 s
Channel: Daniel Mcconnell
Description: Graph the linear system and estimate the solution. Then check the solution algebraically. y=-3 x-2 5 x+2 y=-2

   Graph the linear system and estimate the solution. Then check the solution algebraically.
$\begin{aligned} & y=-3 x-2 \\ & 5 x+2 y=-2\end{aligned}$

McDougal Littell Algebra 2

Holt McDougal, Ron… 9th Edition

Chapter 3, Problem 9

Instant Answer

Solved by Expert Daniel Mcconnell

06/26/2020

Step 1

This is in slope-intercept form $ y = mx + b $, where the slope $ m = -3 $ and the y-intercept $ b = -2 $. To graph this line, start at the point (0, -2) on the y-axis. From there, use the slope to find another point: move down 3 units and right 1 unit to Show more…

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Graph the linear system and estimate the solution. Then check the solution algebraically. $\begin{aligned} & y=-3 x-2 \\ & 5 x+2 y=-2\end{aligned}$

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Key Concepts

Linear Systems

A linear system is a collection of two or more linear equations involving the same set of variables. The solution to the system is the set of variable values that satisfy all equations simultaneously.

Graphical Method

The graphical method involves plotting each equation on a coordinate plane to see where the corresponding lines intersect. This intersection point, if it exists, represents the solution to the system.

Intersection Point

The intersection point of the graph represents the values of the variables where both equations are satisfied. In a two-equation system, this point is the unique solution when the lines are not parallel.

Algebraic Verification

Algebraic verification involves solving the system using methods like substitution or elimination to confirm that the solution obtained from the graph accurately satisfies all the equations in the system.

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