Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, of allinfinite number of solutions. If the system has one solution, find the solution.4x + 2y = -2010x + 5y = -50

Solve The Following System Of Linear Equations By Substitution And Determine Whether The System Has One Solution No Solution Of Allinfinite Number Of Solutions class=

Sagot :

[tex]\begin{gathered} 4x+2y=-20 \\ 10x+5y=-50 \end{gathered}[/tex]

To solve the above system of equation, let's use substitution method. Here are the steps:

1. Equate second equation to y = .

[tex]\begin{gathered} 10x+5y=-50 \\ 5y=-10x-50 \\ \text{Divide both sides by 5.} \\ \frac{5y}{5}=-\frac{10x}{5}-\frac{50}{5} \\ y=-2x-10 \end{gathered}[/tex]

2. Use this value of "y" and plug it in to the first equation.

[tex]\begin{gathered} 4x+2y=-20 \\ 4x+2(-2x-10)=-20 \end{gathered}[/tex]

Then, solve for x.

[tex]\begin{gathered} 4x-4x-20=-20 \\ \text{Add 20 on both sides.} \\ 4x-4x-20+20=-20+20 \\ 0=0 \end{gathered}[/tex]

It seems like both equations are just equal to each other. With this, the system has infinite number of solutions.

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.