Solve the system by the method of substitution. { (1)/(5) x+(1)/(2) y=8 x+y=20 .

Name: Problem 21, Chapter 7: Precalculus
Uploaded: 2021-02-16T18:44:14-08:00
Duration: 2 min 25 s
Channel: Swati Agarwal
Description: Solve the system by the method of substitution. { (1)/(5) x+(1)/(2) y=8 x+y=20 .

step 1 Over here, a system of equations has been given to us. The first equation is 1 upon 5x plus 1 up

Solve the system by the method of substitution. { ...

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 consists of two or more equations that share the same set of variables. The goal is to find a set of values for the variables that satisfies all the equations simultaneously. This concept is fundamental in algebra and is used to determine the point or points of intersection between lines or planes.

Method of Substitution

The method of substitution is a technique for solving a system of equations by isolating one variable in one of the equations and substituting the resulting expression into the other equations. This reduces the number of variables step by step, ultimately leading to a solution that satisfies the entire system.

Handling Fractions in Equations

When equations include fractional coefficients, it is important to manage these fractions carefully to simplify the equations. Techniques such as clearing denominators by multiplying through by a common multiple can be employed, or one can directly substitute expressions involving fractions, ensuring that all operations adhere to the properties of equality.

Transcript

Please give Ace some feedback