Solving Systems of Equations

The video tutorial explains how to solve a system of equations using the elimination method, also known as the addition method. It covers converting equations to standard form, choosing which variable to eliminate, and performing calculations to find the values of X and Y. The tutorial also demonstrates back substitution to verify the solution and discusses the consistency and independence of the equations. The solution is verified by substituting the values back into the original equations and checking the results.

What is the primary goal of using the elimination method in solving a system of equations?

• To determine the y-intercept

• To eliminate all variables

• To find the intersection point of two lines

• To find the slope of the lines

What is the first step in preparing equations for the elimination method?

• Finding the slope

• Putting equations in standard form

• Graphing the equations

• Calculating the y-intercept

When preparing to eliminate a variable, what must be true about the coefficients of that variable?

• They must be positive

• They must be zero

• They must be opposites

• They must be equal

What is the result of adding the equations after eliminating the Y terms?

• A new equation with only X terms

• A new equation with only Y terms

• A new equation with both X and Y terms

• A new equation with no variables

After finding the value of X, what is the next step in solving the system?

• Substitute X back into one of the original equations

• Check the solution with a calculator

• Graph the equations

• Eliminate the X terms

What does it mean if a system of equations is consistent?

• It has infinite solutions

• It has at least one solution

• It has exactly two solutions

• It has no solutions

What is the ordered pair solution for the given system of equations?

• (-5, -1/2)

• (-5, 1/2)

• (5, 1/2)

• (5, -1/2)

How can you verify the solution of a system of equations?

• By using a calculator

• By calculating the determinant

• By finding the slope

• By checking the solution graphically

What is the significance of the ordered pair (5, -1/2) in the context of the system of equations?

• It is the midpoint of the two lines

• It is the x-intercept of the lines

• It is the point of intersection of the two lines

• It is the y-intercept of the lines

What method can be used to check the solution besides substitution?

• Graphing the equations

• Finding the slope

• Calculating the determinant

• Using a calculator