10.1 Systems of Equations
TYPEWRITER
What is the longest word that can be typed by only using
the top row of letters on a typewriter???
Systems of Equations
Recall the three ways to solve systems of equations.
Solve using substitution.
 2x  y  5

4 x  6y  2
Systems of Equations
Solve using elimination.
5x  3y  7

3x  5y  23
System Solutions
Consistent System
Independent Equations
Consistent System
Dependent Equations
Inconsistent System
Systems of Equations
Use the method of your choosing to solve the following.
x  y  5
 2x  5y  3


3x  3y  2
6x 15y  9

Application
A movie theater charges $9.00 for adults and $7.00 for
senior citizens. On a day when 325 people paid an
admission, the total receipts were $2495. How many who
paid were adults? How many were seniors?
Systems of Three Equations
Solve.
4 x  3y  2z  16
x  y  z  1
4 x  3y  2z  16

 x  y  z  1

2x  2y  3z  5


x  y  z  1
2x  2y  3z  5
Systems of Three Equations
 x  y  z  4

2x  3y  4z  15

 5x  y  2z  12
Solve.

System Solutions
Consistent System
Indep. Equations
Consistent System
Depend. Equations
Inconsistent System
Systems of Three Equations
2x  3y  z  0

3x  2y  2z  2

 x  5y  3z  2
Solve.

10.1 Systems of Equations
Homework #24:
p.738 #31, 35,
43, 53