Solving Systems of Equations Using Elimination

In this video, Miss Smith explains the elimination method for solving systems of equations. She covers the ideal conditions for using elimination, such as when equations are in standard form. The video includes multiple examples demonstrating how to create elimination situations by adjusting equations and using the crisscross method. Special cases like infinite solutions and no solution are also discussed, providing a comprehensive understanding of the elimination strategy.

What is the ideal form of equations for using the elimination method?

• Point-slope form

• Vertex form

• Standard form

• Slope-intercept form

What does 'same but opposites' refer to in the context of the elimination method?

• Equations with the same slope but opposite y-intercepts

• Coefficients of either x or y that are equal in magnitude but have opposite signs

• Constants on the right side of the equation that are opposites

• Equations that are inverses of each other

How do you create 'same but opposites' when they are not initially present?

• By dividing one or both equations by a constant

• By adding equations together

• By multiplying one or both equations by a constant

• By subtracting one equation from the other

What is the next step after creating 'same but opposites' and eliminating one variable?

• Check the solution in both original equations

• Rewrite the equations in slope-intercept form

• Graph the equations

• Solve for the remaining variable

How do you find the value of the second variable after eliminating the first one?

• By multiplying the remaining equation by the eliminated variable

• By setting the remaining variable equal to zero

• By graphing the remaining equation

• By substitution into one of the original equations

When multiplying an equation to create 'same but opposites', what must you remember to do?

• Only multiply the constants

• Multiply every term in the equation

• Multiply only one side of the equation

• Multiply only the variable terms

In the context of elimination, what is the best strategy when both variables have the same coefficient but are not opposites?

• Graph the equations to find the solution

• Multiply one equation by -1

• Switch to the substitution method

• Add the two equations as they are

What does it mean if, after elimination, you get a true statement like 0=0?

• There is no solution

• The equations are undefined

• There is exactly one solution

• There are infinitely many solutions

What does it indicate if, after elimination, you end up with a false statement like 0=10?

• The equations are dependent

• The system has no solution

• The system has infinitely many solutions

• The system has one unique solution

What is the final step after finding the values of both variables in a system of equations?

• Plot the solution on a graph

• Substitute the values back into the original equations to check

• Multiply the variables to find the product

• Add the variables to find the sum