Exploring the Substitution Method for Systems of Equations

When is the substitution method most useful?

• When the equations are nonlinear

• When the equations are in standard form

• When one variable is close to being isolated

• When both variables are already isolated

In the first example, what is the value of x after substitution?

• 4

• 5

• 3

• 2

What is the final solution to the system in the first example?

• (4, 8)

• (1, 2)

• (3, 6)

• (2, 4)

In the second example, what is the first step to isolate x?

• Subtract 2y from the other side

• Add 2y to the other side

• Divide both sides by 2

• Multiply both sides by 2

What is the y-coordinate of the solution in the second example?

• 3

• 2

• 4

• 1

In the third example, what happens when you solve the equation after substitution?

• The variables cancel out and you get a false statement

• You get infinitely many solutions

• You get a unique solution

• The variables cancel out and you get a true statement

What does it mean when the variables cancel out and you get a false statement?

• The system is inconsistent

• There is a unique solution

• There are infinitely many solutions

• There is no solution

In the final example, what is the y-coordinate of the solution?

• -9

• -6

• -8

• -7

What is the x-coordinate of the solution in the final example?

• -23

• -21

• -22

• -20

When is the elimination method preferred over substitution?

• When the equations are in standard form and aligned

• When the equations are nonlinear

• When both variables are already isolated

• When one variable is close to being isolated