Substitution Method in Solving Equations

The video tutorial covers solving systems of equations using the substitution method. It begins with an introduction to the method and demonstrates solving two examples. The first example involves a straightforward substitution where one equation is already solved for a variable. The second example requires additional steps to solve for a variable before substitution. The tutorial emphasizes careful handling of signs and symbols, combining like terms, and graphing the equations to find solutions.

What is the first step in solving a system of equations using substitution when one variable is already isolated?

• Add the equations together.

• Substitute the isolated variable into the other equation.

• Graph the equations.

• Multiply both equations by a constant.

In Example 1, what is the value of y when x is -2?

• -4

• 2

• 4

• -2

Why is it important to be careful with symbols and signs during substitution?

• To avoid incorrect solutions.

• To simplify the equations.

• To make the process faster.

• To ensure the equations are balanced.

What is the solution to the system of equations in Example 1?

• x = -2, y = -4

• x = 2, y = -4

• x = -2, y = 4

• x = 2, y = 4

What additional step is required in Example 2 that was not needed in Example 1?

• Graphing the equations.

• Solving for one variable first.

• Multiplying the equations by a constant.

• Adding the equations together.

In Example 2, what is the expression for x after isolating it in the first equation?

• x = 7 + 3y

• x = 7 - 3y

• x = 3y - 7

• x = -7 + 3y

What is the value of y in Example 2 after solving the system of equations?

• 1

• 3

• 0

• 2

What operation is performed after substituting the expression for x in Example 2?

• Subtraction

• Division

• Addition

• Distribution

What is the final solution for the system of equations in Example 2?

• x = 1, y = 2

• x = 1, y = 3

• x = 3, y = 2

• x = 2, y = 1

What is the purpose of dividing each side by -10 in Example 2?

• To eliminate fractions.

• To isolate the variable y.

• To check the solution.

• To simplify the equation.