Use the elimination method to solve the system. (3)/(x)+(2)/(y)=-7 (1)/(x)-(4)/(y)=-14

Name: Problem 28, Chapter 11: Contemporary Precalculus
Uploaded: 2020-07-17T19:38:14-08:00
Duration: 2 min
Channel: Christopher Stanley
Description: Use the elimination method to solve the system. (3)/(x)+(2)/(y)=-7 (1)/(x)-(4)/(y)=-14

step 1 All right, let's solve the system of equations. Now I do this, let me multiply this top equation

Use the elimination method to solve the system. ...

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Key Concepts

System of Equations

A system of equations consists of two or more equations with the same set of unknowns, and the solution to the system is the set of values for the variables that satisfies all of the equations simultaneously. Understanding these systems is fundamental for algebra, as they appear frequently in various contexts in mathematics and applied fields.

Elimination Method

The elimination method is a technique for solving systems of equations where you add or subtract equations to cancel one of the variables, making it easier to solve for the remaining variable. By strategically multiplying one or both equations, you align coefficients so that one variable is eliminated when the equations are combined, simplifying the solution process.

Substitution of Reciprocals

In problems where variables appear as denominators, it is often helpful to substitute the reciprocals of the original variables with new variables. This transforms the equations into a more typical linear system, enabling the use of established methods like elimination or substitution to solve the system effectively.

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