Solving Systems of Equations by Elimination

The video tutorial explains how to solve systems of equations using the elimination method. It compares graphing and algebraic methods, focusing on elimination for exact solutions. The tutorial covers the need for opposite coefficients and how to use multipliers to achieve them. An example problem is provided to demonstrate the process, including finding the least common multiple and solving the system. The solution is verified by graphing to ensure accuracy.

What is a system of equations?

• A set of unrelated equations

• Two or more equations with the same variables

• A single equation with multiple variables

• An equation with no variables

Which method is typically used for estimating solutions to systems of equations?

• Factoring

• Substitution

• Graphing

• Elimination

What is the goal of using elimination in solving systems of equations?

• To simplify to one equation with one variable

• To multiply both equations by the same number

• To find the least common multiple

• To graph the equations

What do you need to achieve for elimination to work effectively?

• Opposite coefficients for one variable

• Same coefficients for all variables

• No coefficients for any variable

• Equal coefficients for all variables

How do you find the least common multiple of two numbers?

• By finding the smallest multiple common to both

• By dividing the larger number by the smaller

• By adding the numbers

• By subtracting the smaller number from the larger

What is the solution to a system of equations?

• A single number

• A coordinate point that satisfies each equation

• A graph of the equations

• A set of unrelated numbers

Why is it beneficial to verify the solution of a system of equations with a graph?

• To find the least common multiple

• To ensure the point of intersection is correct

• To simplify the equations

• To eliminate variables