Adding Equations in a System: Using the Addition Property of Equality

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 solutions by testing number pairs and verifying them by adding equations. The tutorial emphasizes that adding the same value to both sides of an equation maintains its truth, and this principle is applied to solve systems of equations.

What does the addition property of equality state?

• Adding the same value to both sides of an equation results in a true equation.

• Subtracting the same value from both sides of an equation results in a false equation.

• Adding different values to both sides of an equation results in a true equation.

• Multiplying both sides of an equation by different values results in a true equation.

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

• (1, 4)

• (2, 3)

• (3, 2)

• (4, 1)

Why is the pair (3, 2) a solution to the system x + y = 5 and x - y = 1?

• It satisfies only the second equation.

• It satisfies neither equation.

• It satisfies only the first equation.

• It satisfies both equations.

What happens when you add the equations x + y = 5 and x - y = 1?

• You get 2x = 6, which confirms x = 3.

• You get 2x = 5, which confirms x = 2.5.

• You get 2x = 7, which confirms x = 3.5.

• You get 2x = 4, which confirms x = 2.

In the system y = 2x - 3 and x - 2y = 0, what is the solution?

• (0, 3)

• (3, 0)

• (2, 1)

• (1, 2)

How do you verify that (2, 1) is a solution to the system y = 2x - 3 and x - 2y = 0?

• By substituting into neither equation.

• By substituting into both equations and checking for true statements.

• By substituting into only the second equation.

• By substituting into only the first equation.

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

• x - y = 2x - 3

• x + y = 2x - 3

• x - y = 3x - 3

• x + y = 3x - 3