Understanding the Substitution Method in Solving Systems of Equations

The video tutorial explains how to solve systems of equations using the substitution method. It begins by introducing the concept of substitution, where one variable is isolated and replaced in another equation. The tutorial demonstrates solving two different systems of equations, first finding the y-value and then using it to find the x-value. The process involves identifying like terms, distributing, and performing basic algebraic operations to isolate variables and find solutions in the form of ordered pairs.

What is the primary purpose of the substitution method in solving systems of equations?

• To graph the equations

• To solve for one variable in terms of another

• To find the slope of the line

• To eliminate all variables

When using the substitution method, what is the first step?

• Graph the equations

• Add the equations together

• Multiply both equations

• Look for an isolated variable

In the substitution method, what do you do after finding an expression for one variable?

• Graph the expression

• Ignore the expression

• Substitute it into the other equation

• Solve for the same variable again

What operation is used to isolate the variable after combining like terms?

• Division

• Multiplication

• Subtraction

• Addition

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

• (2, 4)

• (2, 8)

• (8, 2)

• (4, 2)

In the second problem, what expression is substituted for y?

• 3x + 5

• x + 7

• 4x + 2

• 2x - 1

What is the result of distributing the positive two in the second problem?

• -2x - 14

• 2x - 14

• -2x + 14

• 2x + 14

After combining like terms in the second problem, what is the equation?

• 4x - 14 = 20

• 2x - 14 = 20

• 4x + 14 = 20

• 2x + 14 = 20

What is the x-coordinate of the solution in the second problem?

• 3

• 5

• 4

• 2

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

• (3, 2)

• (2, 3)

• (4, 3)

• (3, 4)