Number of Solutions in Systems of Equations

Systems of Linear Equations Word Problem Practice Guide

Multiple Choice

What types of solution is NOT possible for solving systems of linear equations?

• No Solution

• One Solution

• Two Solutions

• Infinite Solutions

Multiple Choice

The ordered pair that satisfies all equations in the system.

• system of equations
• function
• graph
• solution of a system

​Algebraically, this looks like...

• ​No Solution

  • ​variables cancel, untrue statement

  • ex) 3 = 5

• ​One solution

  • ​Able to solve for x and y

  • ex) (1, 9)

• ​Infinite Solution

  • ​variables cancel, true statement

  • ​ex) -1 = -1

Multiple Choice

When solving a system algebraically, which expression indicates there is 1 solution?

• 2=2

• -2=6

• x=7

• 0=0

Multiple Choice

When solving a system algebraically, which expression indicates there is no solution?

• $$4=-2$$

• $$y=0$$

• $$0=0$$

• $$x=2$$

Multiple Choice

When solving a system algebraically, which expression indicates there are infinite solutions?

• $$9=8$$

• $$x=0$$

• $$-3=-3$$

• $$y=4$$

​Graphically, this looks like...

• ​No Solution

  • ​parallel lines

• ​One solution

  • ​Intersecting lines

• ​Infinite Solution

  • ​one line

Multiple Choice

How many solutions?

• One Solution
• No solution
• Infinitely Many Solutions

Multiple Choice

What is the number of solutions to the system of equations?

• No Solution

• Infinitely Many Solutions

• One Solution

• Two Solutions

Multiple Choice

What is the solution to the system?

• (0, 3)
• (1, -1)
• (-3, 1)
• (1, 3)

Determining the best method to solve...

• Graphing

  • if a graph is provided

  • both equations start with y =

  • easy to find the x and y intercepts graphically

• ​Substitution

  • if the question says to solve algebraically​

  • at least one equation starts with y = or x =

• Elimination

  • ​if the question says to solve algebraically​

  • ​in standard form of Ax + By = C

Multiple Choice

Which is the best method for solving this system of equations?

-4x-2y=-12

4x+8y=-24

• Substitution

• Elimination

• Graphing

Multiple Choice

Which is the best method for solving this system of equations?

• Substitution

• Graphing

• Elimination

Multiple Choice

Which is the best method for solving this system of equations?

2x - y = 0

4x - y = 0

• Substitution

• Elimination

• Graphing

Multiple Choice

Which is the best method for solving this system of equations?

8x + 4y = 12

y = -2x + 3

• Substitution

• Graphing

• Elimination

Graphing Systems Word Problems

• Read the text (more than once!)

• Write the Let Statements

• Set up two (2) equations

• ​Decide what type of solving would be best

  • ​Algebraically -> Substitution or Elimination

  • ​Graphically -> Use the table in the calculator

• Answer the question

Practice Problem:

You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject?

We don't know how many math or science problems so we are going to assign variables.

​

Let x = # Science problems

y = # Math problems

​

Multiple Choice

How many TOTAL problems do you have?

You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject?

• 42

• 10

Fill in the Blanks

Using the information of 42 total problems, and our variables x & y write an equation that represents adding up all of our total problems.

You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject?

Fill in the Blanks

What's the 2nd equation? Remember, you have 10 more math problems than science problems.

Science problems = x

Math problems = y

You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject?

Poll

Now it's time to solve the system. Which method would you use to solve

$$x+y=42$$   $$y=x+10$$  

• Graphing

• Elimination

• Substitution

​Personally I would use substitution or graphically for this problem.

​

​Choose whichever method you would like though and lets see if you are able to find out the value of x and y!

​

​Solve this now please.

​

​You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject?

Fill in the Blanks

How many science problems are there? Write only a number as your answer. Remember, 

x = science problems

y = math probems

$x+y=42$   $y=x+10$  

Fill in the Blanks

How many math problems are there? Write only a number as your answer. Remember, 

x = science problems

y = math problems

$x+y=42$   $y=x+10$