Question

Solve the system using the substitution method. For systems that do not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent. $$\begin{aligned}&5 x-2 y=-25\\&10 x=3(y-10)\end{aligned}$$

Name: Problem 50, Chapter 3: Intermediate Algebra
Uploaded: 2020-06-21T14:25:56-08:00
Duration: 2 min 30 s
Channel: Christopher Stanley
Description: Solve the system using the substitution method. For systems that do not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent. 5 x-2 y=-25 10 x=3(y-10)

   Solve the system using the substitution method. For systems that do not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent.
$$\begin{aligned}&5 x-2 y=-25\\&10 x=3(y-10)\end{aligned}$$

Intermediate Algebra

Julie Miller, Molly… 5th Edition

Chapter 3, Problem 50

Instant Answer

Solved by Expert Christopher Stanley

06/21/2020

Step 1

We can do this by adding $2y$ to both sides of the equation: \[5x = -25 + 2y\] Then, we can multiply the whole equation by $2$ to get: \[10x = -50 + 4y\] Show more…

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Solve the system using the substitution method. For systems that do not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent. $$\begin{aligned}&5 x-2 y=-25\\&10 x=3(y-10)\end{aligned}$$

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Key Concepts

Systems of Linear Equations

This concept involves two or more linear equations that share common variables. Solving such systems means finding all variable values that satisfy every equation simultaneously, and this approach is fundamental in algebra and linear algebra.

Substitution Method

The substitution method is a technique where one equation is solved for one variable in terms of the others, and that expression is substituted into the remaining equations. This reduces the problem to a system with fewer variables, making it easier to solve.

Consistency and Dependency

When analyzing a system of linear equations, it is important to determine whether the system has a unique solution (consistent and independent), infinitely many solutions (consistent and dependent), or no solution (inconsistent). This concept is central to understanding the nature and behavior of systems in algebra.

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