Solving Systems of Equations by Elimination

Why is it important to know both the substitution and elimination methods?

• Because they are both required for the final exam.

• Because one method is always better than the other.

• Because some systems are easier to solve with one method over the other.

• Because the teacher prefers the elimination method.

What is the first step in the elimination method?

• Ensure the variables are lined up.

• Isolate one variable.

• Multiply the equations.

• Add the equations together.

In the first example, what happens when you add the equations together?

• Both variables cancel out.

• The y variables cancel out.

• The x variables cancel out.

• Neither variable cancels out.

After finding x in the first example, what is the next step?

• Find y by isolating it in the same equation.

• Find y by substituting x into either original equation.

• Find y by adding the equations again.

• Find y by multiplying the equations.

What should you do if the variables do not cancel out when you add the equations?

• Switch to the substitution method.

• Add a constant to one of the equations.

• Subtract the equations instead.

• Multiply one or both equations to make the coefficients match.

In the second example, why do you multiply one of the equations by -1?

• To make the coefficients of x match.

• To simplify the equation.

• To make the coefficients of y match.

• To eliminate the constant term.

What is the result when you add the modified equations in the second example?

• y equals 3

• x equals -1

• y equals -1

• x equals 3

In the third example, what do you multiply the top equation by to cancel out the y variable?

• 3

• 5

• 4

• 2

What does it mean if both sides of the equation cancel out to 0?

• The system is inconsistent.

• There is no solution.

• There are infinitely many solutions.

• The system is dependent.

What should you do if you end up with an equation like 0 = 5?

• The system is dependent.

• There is no solution.

• There are infinitely many solutions.

• The system is consistent.