Question

In the following exercises, determine if the following points are solutions to the given system of equations. $$ \left\{\begin{array}{l} 2 x-6 y=0 \\ 3 x-4 y=5 \end{array}\right. $$ (a) (3,1) (b) (-3,4)

Name: Problem 1, Chapter 5: Elementary Algebra
Uploaded: 2022-09-24T21:16:21-08:00
Duration: 1 min 11 s
Channel: Erika Bustos
Description: In the following exercises, determine if the following points are solutions to the given system of equations. { 2 x-6 y=0 3 x-4 y=5 . (a) (3,1) (b) (-3,4)

   In the following exercises, determine if the following points are solutions to the given system of equations.
$$
\left\{\begin{array}{l}
2 x-6 y=0 \\
3 x-4 y=5
\end{array}\right.
$$
(a) (3,1) (b) (-3,4)

Elementary Algebra

Lynn Marecek 1st Edition

Chapter 5, Problem 1

Instant Answer

Solved by Expert Erika Bustos

09/24/2022

Step 1

Substitute $x = 3$ and $y = 1$: \[2(3) - 6(1) = 0\] \[6 - 6 = 0\] \[0 = 0\] The point (3, 1) satisfies the first equation. Show more…

Show all steps

Thanks for your feedback!

In the following exercises, determine if the following points are solutions to the given system of equations. $$ \left\{\begin{array}{l} 2 x-6 y=0 \\ 3 x-4 y=5 \end{array}\right. $$ (a) (3,1) (b) (-3,4)

Play audio

Feedback

Erika Bustos and 82 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

System of Linear Equations

A system of linear equations is a set of two or more equations involving the same set of variables. In a two-variable system, each equation represents a line in the coordinate plane, and the solution to the system is the point or points where these lines intersect. Solving such systems involves finding the values of the variables that satisfy all the equations simultaneously.

Verification of a Proposed Solution

Verification of a proposed solution involves substituting the candidate values for the variables back into each equation of the system to check if the equations hold true. If the computed result matches the expected value in every equation, the candidate is a solution; if not, it fails to satisfy the system. This process is essential for ensuring that a given point is indeed the intersection of all corresponding equations.

Please give Ace some feedback