Solving Systems of Equations by Elimination

What is the key difference between solving systems of equations using substitution versus elimination?

• Substitution involves only one equation, while elimination uses two.

• Elimination involves adding equations, substitution does not.

• Elimination can only be used with linear equations.

• Substitution requires opposites, while elimination does not.

What is the purpose of the elimination method in solving systems of equations?

• To graph the equations more easily.

• To eliminate one variable to simplify solving for the other.

• To find the value of one variable first.

• To demonstrate multiple solutions exist.

What is essential for using the elimination method effectively?

• Solving for one variable at a time.

• Identifying or creating opposites in the equations.

• Using a calculator for complex calculations.

• Having equations in the form ax + by = c.

What is the result of adding two equations with opposites in the elimination method?

• A new equation is formed without elimination.

• One variable is eliminated.

• The equations become dependent.

• Both variables are eliminated.

What do you do after eliminating one variable in the elimination method?

• Solve for the remaining variable.

• Eliminate the second variable.

• Rewrite the equations in standard form.

• Graph the equations.

How do you solve a system of equations by elimination when opposites are not immediately present?

• By dividing the equations.

• By multiplying one or both equations to create opposites.

• By graphing the equations to find the intersection point.

• By substituting one equation into the other.

When is it more challenging to use the elimination method?

• When the equations are in standard form.

• When the coefficients of both variables are the same.

• When the system has no solution.

• When there are no opposites present initially.

Why is it sometimes necessary to multiply equations in the elimination method?

• To convert the equations into standard form.

• To reduce the number of steps needed.

• To create opposites for elimination.

• To simplify the equations.

How can you check if your solution to a system of equations is correct?

• By consulting a calculator.

• By graphing the solution.

• By solving the system using another method.

• By substituting the solution back into the original equations.

What is the final step after solving for both variables in the elimination method?

• Checking the solution by plugging it back into the original equations.

• Solving the system again using substitution.

• Graphing the solution on a coordinate plane.

• Multiplying the solution by the least common multiple.