Solving Systems of Linear Equations

This video tutorial explains how to solve systems of linear equations using the substitution method. It begins with an introduction to the concept and success criteria, followed by two detailed examples demonstrating the step-by-step process of solving systems by substitution. The tutorial concludes with a real-world word problem involving the purchase of burgers, illustrating the practical application of the method.

What is the primary goal when using the substitution method to solve a system of linear equations?

• To obtain an equation in one variable and solve it

• To graph the equations and find the intersection point

• To eliminate one variable by adding the equations

• To multiply the equations by a common factor

In the first example, what is the initial isolated variable?

• None of the above

• z

• y

• x

After substituting the value of y in the first example, what is the resulting equation?

• 7x - 2(2x - 4) = 5

• 7x + 2y = 5

• 2x - 4 = y

• x + y = 5

What is the solution to the system of equations in the first example?

• (1, 6)

• (-6, -1)

• (-1, -6)

• (0, 0)

In the second example, why is it beneficial to isolate the variable y?

• Because y is already solved for

• Because y does not have a coefficient

• Because y has the smallest coefficient

• Because y is the first variable in the equation

What is the final solution to the system of equations in the second example?

• (3/2, -2)

• (2/3, 2)

• (-2, 3/2)

• (1.5, -2)

In the word problem, what do the variables x and y represent?

• x is the total cost, y is the total number of burgers

• x is the price per burger, y is the total cost

• x is the number of turkey burgers, y is the number of veggie burgers

• x is the number of veggie burgers, y is the number of turkey burgers

What is the first equation derived from the word problem?

• x + y = 90

• 2x + 1.5y = 50

• x + y = 50

• 2x + y = 90

How many turkey burgers were purchased according to the solution of the word problem?

• 30

• 40

• 50

• 20

What is the total cost equation used in the word problem?

• x + y = 90

• 2x + 1.5y = 90

• x + 1.5y = 50

• 2x + y = 50