Labeling a System by Solving Using Elimination Method

The video tutorial explains how to handle equations with different coefficients by choosing appropriate multipliers to eliminate one variable. It demonstrates the process of multiplying equations to achieve opposite coefficients, leading to the elimination of variables. The tutorial concludes with an analysis of the results, showing that if both variables are eliminated, the equations represent parallel lines with no intersection, indicating no solution.

What is the main goal when selecting a multiplier for a system of equations?

• To make one coefficient positive and the other negative

• To increase the value of the coefficients

• To make both coefficients positive

• To eliminate both variables simultaneously

What should you do after multiplying the entire equation by the chosen multiplier?

• Ignore the new equation

• Divide the equations

• Add the equations together

• Subtract the equations

What is the result of adding two equations that have been adjusted to have opposite coefficients for one variable?

• An equation with zero coefficients for both variables

• A solution to the system

• A new equation with a single variable

• An equation with increased coefficients

What does it mean if both variables are eliminated in the process?

• The system has a unique solution

• The system has infinitely many solutions

• The system has no solution

• The system is inconsistent

What type of lines do the equations represent if they have no solution?

• Intersecting lines

• Parallel lines

• Coinciding lines

• Perpendicular lines