Question

In Exercises $1-10$, determine whether the given ordered pair is a solution of the system. $$\begin{aligned} &(5,-2)\\ &\left\{\begin{aligned} 4 x-3 y &=26 \\ x &=15-5 y \end{aligned}\right. \end{aligned}$$

Name: Problem 10, Chapter 4: Introductory and Intermediate Algebra for College Students 4th
Uploaded: 2020-06-08T16:24:29-08:00
Duration: 1 min 1 s
Channel: John Irizar
Description: In Exercises 1-10, determine whether the given ordered pair is a solution of the system. (5,-2) { 4 x-3 y =26 x =15-5 y .

   In Exercises $1-10$, determine whether the given ordered pair is a solution of the system.
$$\begin{aligned}
&(5,-2)\\
&\left\{\begin{aligned}
4 x-3 y &=26 \\
x &=15-5 y
\end{aligned}\right.
\end{aligned}$$

Introductory and Intermediate Algebra for College Students 4th

Robert Blitzer 4th Edition

Chapter 4, Problem 10

Instant Answer

Solved by Expert John Irizar

06/08/2020

Step 1

The first equation is $4x - 3y = 26$. Substituting $x = 5$ and $y = -2$ gives us $4(5) - 3(-2) = 26$. Simplifying this gives us $20 + 6 = 26$, which is true. So, the ordered pair $(5,-2)$ satisfies the first equation. Show more…

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In Exercises $1-10$, determine whether the given ordered pair is a solution of the system. $$\begin{aligned} &(5,-2)\\ &\left\{\begin{aligned} 4 x-3 y &=26 \\ x &=15-5 y \end{aligned}\right. \end{aligned}$$

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Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations involving the same set of variables. Understanding this concept is essential as the system represents multiple constraints that need to be satisfied simultaneously by the solution.

Ordered Pair as a Candidate Solution

An ordered pair is a set of values assigned to the variables of an equation or a system of equations. Identifying whether an ordered pair is a solution involves substituting the pair's values into each equation and checking if all the equations hold true.

Verifying Solutions Using Substitution

The substitution process involves plugging the candidate values for the variables into the equations of the system to determine if the resulting statements are valid. This method is a direct way to check if a proposed solution indeed satisfies all conditions of the system.

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