Solving Systems of Linear Equations

The video tutorial covers solving systems of linear equations using the substitution method. It begins with an introduction to the method, followed by a detailed example. Students are then guided through practice problems, including scenarios where variables are not pre-solved. The tutorial concludes with an advanced practice section and a word problem example, reinforcing the substitution technique.

What is the essential question addressed in this chapter?

• How to use substitution to solve a system of linear equations

• How to graph linear equations

• How to factor quadratic equations

• How to find the slope of a line

What is the first step in solving a system of equations using substitution?

• Multiply the equations by a constant

• Add the equations together

• Solve for one of the variables in one of the equations

• Graph the equations

What do you do after solving for one variable in the substitution method?

• Check the solution in a calculator

• Add the equations together

• Substitute the expression into the other equation

• Graph the solution

In the example problem, what is the value of x when y = -2x - 9 is substituted into 6x - 5y = -19?

• x = 2

• x = 0

• x = -4

• x = 4

What is the solution to the system of equations y = -2x - 9 and 6x - 5y = -19?

• (-4, -1)

• (4, 1)

• (2, -3)

• (0, 0)

When neither equation is solved for a variable, what is a common strategy to avoid fractions?

• Solve for the variable with the smallest coefficient

• Always solve for y

• Solve for the variable with the largest coefficient

• Always solve for x

In the example where no variable is solved, what is the value of x when y = x + 3 is substituted?

• x = 0

• x = -1

• x = 2

• x = 1

What is the solution to the system of equations when y = x + 3 is substituted into the second equation?

• (-1, 2)

• (1, 2)

• (0, 3)

• (2, -1)

In the word problem, what is the relationship between the cost of adult and student tickets?

• Adult tickets cost three times as much as student tickets

• Adult tickets cost half as much as student tickets

• Adult tickets cost twice as much as student tickets

• Adult tickets cost the same as student tickets

What is the price of a student ticket in the word problem?

• $2

• $4

• $6

• $8