Question

Verify that the values of the variables listed are solutions of the system of equations. $$ \begin{aligned} &\left\{\begin{array}{l} {3 x-4 y=4} \\ {\frac{1}{2} x-3 y=-\frac{1}{2}} \end{array}\right.\\ &x=2, y=\frac{1}{2} ;\left(2, \frac{1}{2}\right) \end{aligned} $$

Name: Problem 11, Chapter 12: Algebra and Trigonometry
Uploaded: 2020-06-12T21:18:20-08:00
Duration: 57 s
Channel: Brandon Fox
Description: Verify that the values of the variables listed are solutions of the system of equations. { 3 x-4 y=4 (1)/(2) x-3 y=-(1)/(2) . x=2, y=(1)/(2) ;(2, (1)/(2))

   Verify that the values of the variables listed are solutions of the system of equations.
$$
\begin{aligned}
&\left\{\begin{array}{l}
{3 x-4 y=4} \\
{\frac{1}{2} x-3 y=-\frac{1}{2}}
\end{array}\right.\\
&x=2, y=\frac{1}{2} ;\left(2, \frac{1}{2}\right)
\end{aligned}
$$

Algebra and Trigonometry

Michael Sullivan 10th Edition

Chapter 12, Problem 11

Instant Answer

Solved by Expert Brandon Fox

06/12/2020

Step 1

The first equation is $3x - 4y = 4$. Substituting $x = 2$ and $y = \frac{1}{2}$, we get $3(2) - 4(\frac{1}{2}) = 4$. Simplifying this, we get $6 - 2 = 4$. So, the left-hand side equals the right-hand side, which verifies that the given values are a solution to the Show more…

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Verify that the values of the variables listed are solutions of the system of equations. $$ \begin{aligned} &\left\{\begin{array}{l} {3 x-4 y=4} \\ {\frac{1}{2} x-3 y=-\frac{1}{2}} \end{array}\right.\\ &x=2, y=\frac{1}{2} ;\left(2, \frac{1}{2}\right) \end{aligned} $$

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Key Concepts

Systems of Linear Equations

A system of linear equations consists of multiple equations with common variables, where the goal is to find the set of values that satisfy all equations simultaneously. This concept is fundamental in algebra and allows for the modeling and solving of problems in various fields such as engineering, economics, and physics.

Solution Verification

Verification of a solution involves substituting the proposed values back into each equation of the system to check if the relationships hold true. This process is essential in ensuring that the provided solution is indeed correct and that it satisfies all the equations in the system.

Substitution Method

The substitution method is a technique used to solve or verify systems of equations by replacing the variables with the proposed numerical values. This method not only helps in finding the solution but also reinforces the understanding of how each variable contributes to the equations in the system.

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