Today’s Focus: Solving a system of equations What is a system of equations? A system of equations is when you have two or more equations using the same.

Today’s Focus:

• Solving a system of equations• What is a system of equations?• A system of equations is when you have two

or more equations using the same variables.

• How do we know from reading a problem whether it requires one or two equations?

What does the equation 16x + 10y = 240 represent?

What does the equation x + y = 18 represent?

Worksheet

• Work through parts a, b and c on the worksheet in your groups

Lets talk about problem 1• How did you determine which line matched which

equation?

• How did you determine the solution to the problem?

• Why is the answer an ordered pair?

• How could you check your answers?

What skills are we working on here? How does this tie into the lesson from previous days?

What is a system of equations?

• A system of equations is when you have two or more equations using the same variables.

• The solution to the system is the point that satisfies ALL of the equations. This point will be an ordered pair.

Solving a system of equations by graphing.

Let's summarize! There are 3 steps to solving a system using a graph.

What is the solution of the system graphed below?

1. (2, -2)2. (-2, 2)3. No solution4. Infinitely many solutions

1) Find the solution to the following system:

2x + y = 4x - y = 2

Graph both equations using your calculator

Warm up: Substitution• Fold your paper into four sections (quarters).

You will use one fourth of the paper for your warm up each day. On Thursday I will collect your warm up for points.

• Here is today’s warm up: • 1. Evaluate the following expressions given

the functions below:• g(x) = -3x + 1 f(x) = x2 + 7h(x)=12/x • a. g(10) = b. f(3) = • c. h(–2) = e. h(a)

• Yes, SADLY the STEELERS LOST!

Work on problem 3, parts a and b in your groups

• On your papers explain what actions have been taken since the previous step.

• Once you understand the steps, see if you can answer part c.

Lets compare the method in 3 to the method in problem 4

What is done differently in this problem than in problem 2?

Should this have any effect on the outcome of the problem?

Why not?

In your groups try this…

Solving Systems of Equations using Substitution

Steps:

1. Solve one equation for one variable (y= ; x= ; a=)

2. Substitute the expression from step one into the other equation.

3. Simplify and solve the equation.

4. Substitute back into either original equation to find

the value of the other variable.

5. Check the solution in both equations of the system.

Lets try some more practice

y = 4x3x + y = -21

x + y = 10 5x – y = 2

Seek and Solve

Please put your answer on the bottom right hand corner of your folder. Show your work for full credit!

Warm up:

• Take a few minutes in your group to read the following

• What do the two equations above mean? Be prepared to share your answers!

In your groups complete the worksheet I just handed out.

• In the next problem you will work through the problem step by step to follow the thought process in the elimination method. Take a few minutes to go through the solving by elimination sheet in your packet.

Now complete the systems, equations, and graphs sheet in

your packet

Practice

• Complete each of the ten problems on your worksheet. Your group will then be assigned one problem to put on the chart paper as part of a gallery walk.

• You will need to do all ten problems to receive credit for this activity.

Complete Journal Entry

Warm UP!

• What do you think it means for a system to have infinitely many solutions? What does it mean to be a solution of a system of equations?

In your groups…

Graphic Representation Algebraic Example

Pattern

Infinitely Many Solutions

Now try this…

Graphic Representation Algebraic Example

Pattern

No Solutions

Journal Entry

Warm up!