Contributed by:

Linear functions, equations, and inequalities. The student

applies the mathematical process standards when using

properties of linear functions to write and represent in

multiple ways, with and without technology, linear

equations, inequalities, and systems of equations. The

student is expected to write systems of two linear equations

given a table of values, a graph, and a verbal description.

applies the mathematical process standards when using

properties of linear functions to write and represent in

multiple ways, with and without technology, linear

equations, inequalities, and systems of equations. The

student is expected to write systems of two linear equations

given a table of values, a graph, and a verbal description.

1.

2.
TEKS A.2I

Linear functions, equations, and inequalities. The student

applies the mathematical process standards when using

properties of linear functions to write and represent in

multiple ways, with and without technology, linear

equations, inequalities, and systems of equations. The

student is expected to write systems of two linear equations

given a table of values, a graph, and a verbal description.

Linear functions, equations, and inequalities. The student

applies the mathematical process standards when using

properties of linear functions to write and represent in

multiple ways, with and without technology, linear

equations, inequalities, and systems of equations. The

student is expected to write systems of two linear equations

given a table of values, a graph, and a verbal description.

3.

4.
Career Exploration

• Actuaries

• Actuaries use

mathematics,

statistics, and

financial theory to

analyze the

economic costs of

risk and

uncertainty.

• Actuaries

• Actuaries use

mathematics,

statistics, and

financial theory to

analyze the

economic costs of

risk and

uncertainty.

5.
Linear Equations

• A System of Linear Equations

is:

• a set of 2 or more linear

equations that have the same

set of variables

• A System of Linear Equations

is:

• a set of 2 or more linear

equations that have the same

set of variables

6.
Linear Equations

• When you look at 2 lines on a

graph, those are also what

we call a "system of linear

equations"

• When you look at 2 lines on a

graph, those are also what

we call a "system of linear

equations"

7.
Linear Equations

• The point where 2 lines

intersect (or cross each

other) is what we call

a solution to that system of

equations.

• The point where 2 lines

intersect (or cross each

other) is what we call

a solution to that system of

equations.

8.
Linear Equations

The point (5, -2) is

a solution to this

system of equations,

because that is the

point where these 2

lines cross over each

The point (5, -2) is

a solution to this

system of equations,

because that is the

point where these 2

lines cross over each

9.
Linear Equations

A system has NO

SOLUTION if:

if 2 lines are parallel

(so they must have

the SAME slope).

Parallel lines

will NEVER cross

over each other.

A system has NO

SOLUTION if:

if 2 lines are parallel

(so they must have

the SAME slope).

Parallel lines

will NEVER cross

over each other.

10.
Let’s Practice!

11.
I do

Is (7, -4) a solution to

this system of

A. Yes

B. No

No, the solution is the

point where the two

lines cross.

Is (7, -4) a solution to

this system of

A. Yes

B. No

No, the solution is the

point where the two

lines cross.

12.
I do

What is the solution to this

system of equations?

(Think- at what point do

these lines cross?)

A. (9, 0)

B. (2, -6)

C. (3, 2)

The correct answer is C

(3,2), the point where the

two lines cross.

What is the solution to this

system of equations?

(Think- at what point do

these lines cross?)

A. (9, 0)

B. (2, -6)

C. (3, 2)

The correct answer is C

(3,2), the point where the

two lines cross.

13.
We do

An actuary graphed these two

equations to show the risk

factors for a hurricane.

Is (-3, 4) a solution to this

system of equations?

A. Yes

B. No

An actuary graphed these two

equations to show the risk

factors for a hurricane.

Is (-3, 4) a solution to this

system of equations?

A. Yes

B. No

14.
We do: Answer

• The correct answer is B no.

• The correct answer is B no.

15.
We do

What is the solution to this

system of equations? (Think-

at what point do these lines

A. (1, 3)

B. (9, 5)

C. (-2, -8)

What is the solution to this

system of equations? (Think-

at what point do these lines

A. (1, 3)

B. (9, 5)

C. (-2, -8)

16.
We do: Answer

• The correct answer is A.

• The correct answer is A.

17.
We do

An actuary read this graph

that shows the risk factors

for an airline.

Is (-2, -1) a solution to this

system of equations?

A. Yes

B. No

An actuary read this graph

that shows the risk factors

for an airline.

Is (-2, -1) a solution to this

system of equations?

A. Yes

B. No

18.
We do: Answer

• The correct answer is A.

• The correct answer is A.

19.
You do

What is the solution to

this system of equations?

A. (9, 3)

B. (0, 0)

C. No Solution

D. (8,5)

What is the solution to

this system of equations?

A. (9, 3)

B. (0, 0)

C. No Solution

D. (8,5)

20.
You do: Answer

• These lines do not intersect, so there is NO SOLUTION!

• These lines do not intersect, so there is NO SOLUTION!

21.
You do

What is the solution?

A. 1

B. -2

C. (1, 2)

D. (1, -1)

What is the solution?

A. 1

B. -2

C. (1, 2)

D. (1, -1)

22.
You do: Answer

• The correct answer is D.

• The correct answer is D.

23.
Lesson Review

• A system of linear equations is just a set of

two or more linear equations. In two

variables (x and y) , the graph of a system

of two equations is a pair of lines in the

plane. The lines intersect at infinitely many

points.

• A system of linear equations is just a set of

two or more linear equations. In two

variables (x and y) , the graph of a system

of two equations is a pair of lines in the

plane. The lines intersect at infinitely many

points.

24.
Extra Practice

How many solutions will this

system have?

A. No solution

B. One Solution

C. I Don't Know

D. Infinitely Many Solutions

How many solutions will this

system have?

A. No solution

B. One Solution

C. I Don't Know

D. Infinitely Many Solutions

25.
Extra Practice Answer

• The correct answer is A no solution because

the lines do not cross.

• The correct answer is A no solution because

the lines do not cross.

26.