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Solving a System by Elimination In Exercises $13-30,$ solve the system by the method of elimination and check any solutions algebraically. $$ \left\{\begin{array}{l}{5 x+3 y=6} \\ {3 x-y=5}\end{array}\right. $$

Name: Problem 15, Chapter 7: Precalculus with Limits
Uploaded: 2021-01-25T04:06:25-08:00
Duration: 2 min 24 s
Channel: Joannie Wang
Description: Solving a System by Elimination In Exercises 13-30, solve the system by the method of elimination and check any solutions algebraically. { 5 x+3 y=6 3 x-y=5 .

   Solving a System by Elimination In Exercises
$13-30,$ solve the system by the method of elimination and
check any solutions algebraically.
$$
\left\{\begin{array}{l}{5 x+3 y=6} \\ {3 x-y=5}\end{array}\right.
$$

Precalculus with Limits

Ron Larson 3rd Edition

Chapter 7, Problem 15

Instant Answer

Solved by Expert Joannie Wang

01/25/2021

Step 1

We can do this by multiplying the second equation by 3. This gives us: $$ \left\{\begin{array}{l}{5 x+3 y=6} \\ {9 x-3 y=15}\end{array}\right. $$ Show more…

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Solving a System by Elimination In Exercises $13-30,$ solve the system by the method of elimination and check any solutions algebraically. $$ \left\{\begin{array}{l}{5 x+3 y=6} \\ {3 x-y=5}\end{array}\right. $$

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Key Concepts

Solution Verification

Solution verification involves substituting the found values of the variables back into the original equations to ensure that they satisfy all the equations in the system. This step confirms the correctness of the solution and helps identify any potential errors in the elimination process.

Linear Systems of Equations

A linear system of equations consists of two or more linear equations involving the same set of variables. The goal is to find a common solution that satisfies all equations simultaneously, and such systems can have a unique solution, infinitely many solutions, or no solution at all.

Method of Elimination

The elimination method is a technique used to solve systems of linear equations by systematically removing variables. This is achieved by adding or subtracting equations (or multiples of them) so that one variable cancels out, allowing for the remaining variable to be solved directly.

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