Isolating Variables in Equations

The video tutorial explains how to solve a system of equations using the substitution method. It begins by introducing the concept of substitution and guides viewers on selecting the easiest variable to isolate. The tutorial then demonstrates isolating a variable, substituting it into another equation, and solving for the remaining variable. Finally, it shows how to find the second variable and concludes with the solution to the system of equations.

What is the main method discussed in the video for solving the system of equations?

• Matrix Method

• Elimination

• Substitution

• Graphing

Why is it important to choose the easiest variable to isolate?

• To make the problem more complex

• To simplify the substitution process

• To avoid using substitution

• To ensure the solution is unique

Which variable is chosen to be isolated in the video?

• x in the first equation

• y in the first equation

• x in the second equation

• y in the second equation

What operation is performed to isolate x in the first equation?

• Dividing both sides by 4

• Subtracting 4y from both sides

• Adding 4y to both sides

• Multiplying both sides by 4

What is the expression for x after isolation?

• x = 4y + 1

• x = 1 + 4y

• x = 1 - 4y

• x = -4y - 1

What is the next step after isolating x?

• Substitute x into the second equation

• Solve for y in the first equation

• Graph the equations

• Check the solution

What is the purpose of substituting the isolated variable into the other equation?

• To eliminate the variable

• To simplify the original equation

• To create an equation with one variable

• To find the value of x

What property is applied to simplify the equation after substitution?

• Associative Property

• Distributive Property

• Identity Property

• Commutative Property

What is the simplified equation after combining like terms?

• -10y + 3 = -12

• -12y + 3 = -10

• -10y - 3 = -12

• -12y - 3 = -10

What is the value of y after solving the simplified equation?

• 1/2

• 2/3

• 5/2

• 3/2