# Linear Equations

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.
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.
3.
4. Career Exploration
• 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
6. 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.
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
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.
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.
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)
(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
• 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)
• The correct answer is A.
17. We do
that shows the risk factors
for an airline.
Is (-2, -1) a solution to this
system of equations?
A. Yes
B. No
• 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)
• 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)
• 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.
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