System of Linear Equations Warm-up

System of Linear Equations Warm-up

By Clare Mang

Open Ended

What are the 3 methods to sovling linear systems?

Draw

Draw the graphs and label the 3 types of solutions to linear systems.

Poll

What method would you use to solve this system?

• Graphing

• Substitution

• Elimination

Poll

What method would you use to solve this system?

• Graphing

• Substitution

• Elimination

Open Ended

If you were going to solve this system by elimination, what would be the first step?

Open Ended

If you were going to solve this system by graphing what would be the first step?

​Let's practice some word problems

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 Blank

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 Blank

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.

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​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 Blank

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 Blank

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

x = science problems

y = math problems

$$x+y=42$$   $$y=x+10$$  

Ok let's see if you can get this next one...

Multiple Choice

There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?

• x + y = 15
  4x + 2y = 44
• 4x + 2y = 15
  x + y = 44
• x = 2y + 44
  4x = y + 15
• 2x - 4y = 44
  x - y = 15

Poll

What is your favorite method to use when solving systems?

• Graphing

• Substitution

• Elimination