Solving Systems of Equations

The video tutorial explains how to solve a system of two equations with two unknowns using the elimination method. It demonstrates the process of scaling equations to cancel out variables, solving for one variable, and substituting back to find the other. The tutorial also verifies the solution and explores alternative methods, such as substitution, to achieve the same result.

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

• To find the determinant of the system

• To eliminate one variable to solve for the other

• To graph the equations

• To factor the equations

Why do we multiply an equation by a constant in the elimination method?

• To change the solution of the equation

• To make the coefficients of one variable equal in both equations

• To simplify the equation

• To convert the equation into a quadratic form

After scaling the second equation by 3, what does it become?

• 3y + 2x = 39

• 3y + 6x = 39

• y + 6x = 39

• 3y + 4x = 39

What is the value of x after eliminating y from the equations?

• x = 3

• x = 5

• x = 11

• x = 13

How do we verify the solution of x and y in the original equations?

• By substituting the values back into the original equations

• By graphing the equations

• By finding the determinant

• By using a calculator

In the alternative method, what do we multiply the second equation by to eliminate x?

• -2

• 2

• -3

• 3

What is the value of y after eliminating x using the alternative method?

• y = 11

• y = 3

• y = 13

• y = 5

What is the result of adding the equations after scaling in the alternative method?

• 5y = 15

• 5y = -15

• Negative 5y = 15

• Negative 5y = -15

What is the final solution for x and y using either method?

• x = 11, y = 13

• x = 3, y = 5

• x = 13, y = 11

• x = 5, y = 3

What is the advantage of using different methods to solve the system of equations?

• It provides multiple solutions

• It confirms the accuracy of the solution

• It changes the original equations

• It simplifies the equations