Solving Systems of Equations

The video tutorial explains how adding equations in a system results in an equation with the same solution, using the addition property of equality. It demonstrates this with examples, showing how to find and verify solutions to systems of equations by adding them together.

What happens when you add two equations in a system?

• The solution changes.

• The solution remains the same.

• The equations become invalid.

• The equations cannot be added.

What does the addition property of equality state?

• Adding the same value to both sides of an equation keeps it true.

• Multiplying both sides of an equation by the same value keeps it true.

• Adding different values to both sides of an equation keeps it true.

• Subtracting the same value from both sides of an equation keeps it true.

In the system x + y = 5 and x - y = 1, which pair is a solution?

• (1, 4)

• (2, 3)

• (3, 2)

• (4, 1)

What is the purpose of testing number pairs in a system of equations?

• To verify the solution satisfies both equations.

• To change the system of equations.

• To eliminate one of the equations.

• To find the sum of the equations.

What is the result of adding x + y = 5 and x - y = 1?

• x = 5

• x = 1

• x = 3

• x = 2

Why is it valid to add equations in a system?

• Because it eliminates variables.

• Because it changes the solution.

• Because it simplifies the system.

• Because of the addition property of equality.

What does combining like terms in x + y and x - y result in?

• 2x

• x - y

• x + y

• 2x + 2y

What is the result of substituting x = 3 into 3 + y = 5?

• y = 1

• y = 2

• y = 3

• y = 4

What is the solution to the system y = 2x - 3 and x - 2y = 0?

• (0, 3)

• (2, 1)

• (3, 0)

• (1, 2)

What is the result of adding y = 2x - 3 to x - 2y = 0?

• x - y = 2x - 3

• x + y = 2x - 3

• x - y = 0

• x + y = 0