Solving Systems of Equations Using Substitution

The video tutorial explains how to use substitution to solve a system of two equations. It begins by introducing the equations 2y = x + 7 and x = y - 4. The tutorial demonstrates substituting y - 4 for x in the first equation, simplifying it to solve for y, and then using the value of y to find x. The solution is verified by substituting the values back into the original equations to ensure they hold true.

What are the two equations given in the problem?

• 2y = x + 7 and x = y - 4

• 2x = y + 7 and y = x - 4

• y = 2x + 7 and x = y + 4

• x = 2y + 7 and y = x - 4

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

• Divide both equations by a constant

• Multiply both equations by a constant

• Add the two equations together

• Rewrite one equation in terms of one variable

When substituting x in the first equation, what expression is used?

• y + 4

• 2y - 4

• y - 4

• 2y + 4

After substituting x in the first equation, what is the simplified form of the equation?

• 2y = y - 7

• 2y = y + 3

• 2y = y - 3

• 2y = y + 7

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

• y = 2

• y = 1

• y = 4

• y = 3

How do you find the value of x once y is known?

• Add y to the first equation

• Substitute y into the second equation

• Subtract y from the second equation

• Substitute y into the first equation

What is the value of x when y is 3?

• x = -1

• x = 1

• x = 0

• x = 2

What is the ordered pair solution to the system of equations?

• (-1, 3)

• (3, -1)

• (-3, 1)

• (1, -3)

How do you verify the solution to the system of equations?

• By substituting the values back into the original equations

• By adding the values to the original equations

• By multiplying the values with the original equations

• By dividing the values by the original equations

Does the solution (x = -1, y = 3) satisfy both original equations?

• Yes, it satisfies both equations

• No, it satisfies only the first equation

• No, it satisfies only the second equation

• No, it satisfies neither equation