Solving Systems of Equations All Three Methods

How is the solution to a system of equations found using the graphical method?

• By identifying the point of intersection of the two equations on the graph.

• By adding the two equations together

• By multiplying the two equations

• By finding the average of the two equations

When is the substitution method most useful in solving a system of equations?

• When both equations are already solved

• When the equations are not related

• When the variables are not known

• When one of the equations can be easily solved for one variable

Compare and contrast the substitution and elimination methods for solving a system of equations.

• Substitution method always leads to the correct solution, while elimination method is unreliable

• Substitution method involves adding the equations together, while elimination method involves multiplying the equations

• Both methods involve manipulating the equations to solve for one variable and then substituting or eliminating that variable to solve for the other variables.

• Substitution method only works for linear equations, while elimination method only works for quadratic equations

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Identify which method for solving systems is being described by this fact:
If one equation is isolated like y = 2x or x = 7 - 4y then this method should be used.

• Graphing

• Substitution

• Elimination (linear combination)

Identify which method for solving systems is being described by this fact: Equations must have like terms "stacked" up vertically, usually written in standard form.

• Graphing

• Substitution

• Elimination (linear combination)

When solving the system, if you get a result of something like 6 = 6 or -2 = -2 and the answer is:

• No Solution

• Infinitely Many Solutions

• Not possible

When using any of the 3 methods to solve a system of linear equations the resulting solution is the same no matter which method is used.

• True; using any method will result in the correct solution.

• False; the solution varies because the solution depends on which method is used.

What is the solution to this system?

• (-2, -2)

• (2, -2)

• (-2,2)

• (2, 2)

What is the solution to the system of equations? 
y = 3x - 8
y = 4 - x

• (3,1)

• (1,3)

• (-3,1)

• (3,-1)