Algebra 37 - Solving Systems of Equations by Elimination

The video tutorial explains how to solve systems of linear equations using the elimination method. It begins with a recap of solving equations using graphs and substitution, then introduces the elimination method, which involves adding equations to eliminate a variable. The tutorial provides examples, including complex scenarios where integer multipliers are needed for both equations. It concludes with a justification of why the elimination method is valid.

What is the graphical representation of the solution to a system of two linear equations?

• The slope of the two graphs

• The point where the two graphs intersect

• The midpoint of the two graphs

• The area between the two graphs

Which method was introduced in this lecture for solving systems of equations?

• Substitution method

• Graphical method

• Matrix method

• Elimination method

In the elimination method, what is the goal when adding two equations?

• To double the coefficients

• To eliminate one of the variables

• To find the average of the equations

• To make the equations identical

After eliminating one variable using the elimination method, what is the next step?

• Multiply the equation by a constant

• Solve for the remaining variable

• Graph the remaining equation

• Add another equation

What is the result of dividing both sides of the equation 9Y = 9 by 9?

• Y = -1

• Y = 9

• Y = 1

• Y = 0

What is a potential challenge when using the elimination method?

• No integer multiplier can eliminate a variable

• Equations have no solution

• Equations are too simple

• Variables are already eliminated

How can you overcome the challenge of not having an integer multiplier for elimination?

• Use a calculator

• Choose multipliers for both equations

• Ignore the problem

• Switch to the substitution method

What happens when you add two equations in the elimination method?

• You get a new equation with the same solution set

• The equations become identical

• You get a new equation with a different solution set

• The equations cancel each other out

Why is it acceptable to add two equations in the elimination method?

• Because it changes the solution set

• Because both sides of the second equation are equal

• Because it simplifies the equations

• Because it eliminates all variables

What will be discussed in the next lecture?

• The matrix method

• The graphical method

• The substitution method

• The reasoning behind the elimination method