Adding and Multiplying Equations in a System of Equations

The video tutorial explains how to solve systems of equations by adding a multiple of one equation to another. It begins with an introduction to the concept, followed by a review of the multiplication and addition properties of equality. The tutorial then demonstrates solving a system of equations using trial and error, and further explores the method of multiplying and adding equations to find solutions. The lesson concludes by summarizing the key points and confirming that the solution remains consistent when equations are manipulated in this way.

What does the multiplication property of equality state?

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

• Subtracting the same number from both sides of an equation results in a true equation.

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

• Multiplying both sides of an equation by the same number results in a true equation.

Which number pair is the solution to the system x + y = 5 and x - y = 1?

• (4, 1)

• (3, 2)

• (2, 3)

• (1, 4)

What happens when you multiply one equation by a constant and add it to another equation in a system?

• The solution to the system changes.

• The system becomes unsolvable.

• The resulting equation has a different solution.

• The resulting equation has the same solution as the original system.

If you multiply the equation x - y = 1 by 3, what is the new equation?

• 3x - y = 3

• 3x + 3y = 3

• 3x - 3y = 3

• x - 3y = 3

After adding the equations x + y = 5 and 3x - 3y = 3, what is the resulting equation?

• 4x - 2y = 8

• 4x + 2y = 8

• 2x - 4y = 8

• 2x + 4y = 8