Three Methods for Solving Linear Systems

Solve by elimination:

2x + 9y = -7

6x - 3y = 9

• (-1, -1)

• (2,-1)

• (1,1)

• (1,-1)

Using the elimination method, determine the solution to the system below.

• x = 10, y = -1

• x = -1, y = 10

• x = 3, y = -4

• x = 6, y = 7

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

The first step in solving using the substitution method is __________.

• get x by itself

• get y by itself

• get either variable by itself

• add the equations together

What is the substitution method used for in solving a system of equations?

• To solve a system of equations

• To write a novel

• To calculate the area of a circle

• To bake a cake

In the elimination method, what operation is used to eliminate one of the variables?

• Multiplication

• Addition or subtraction

• Division

• Exponentiation

What are the steps involved in solving a system of equations using the elimination method?

• Identifying the variable to eliminate, multiplying the equations by appropriate constants, and adding or subtracting the equations to eliminate the variable.

• Dividing the equations by random numbers

• Ignoring one of the equations

• Solving for the variable with no elimination

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

Which methods can be used to SOLVE a systems application problem?

• Graphing method

• Substitution method

• Elimination method

• None of these methods

Answer explanation

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