Unit 1
SOLVING SYSTEM OF EQUATIONS
System of equations
 Define: system of equations- a set of two or
more equations
 Define: solution of a system- ordered pair(s)
that make all the equations true.
 Key concept: the solution to a system is where the
graphs intersect.
Lines intersect
1 solution
Lines are Parallel
No solution
Lines coincide
Infinitely many solutions
Solve by graphing
 Solve by graphing:
 Graph in y=
 2nd ,trace, intersection, enter, enter, enter
 y  2x  1

 y  4x  5
y  x  6

2
 y   x  5x  6
System word problem
 Mr. Smith bought 2 lbs of jelly and 3 lbs of peanut
butter. He paid $26.35. Mrs. Sing paid $18.35 for 1.5
lbs of jelly and 2 lbs of peanut butter. What was the
price per pound of each item?
1st write two equations that model the above situation.
~Mr. Smith’s shopping trip
~Mrs. Sing’s shopping trip
2 j  3 p  26.35

1.5 j  2 p  18.35
Then solve the system by graphing. (use CALC)
System of inequalities
 The solution to a system of inequalities is not where
the graphs intersect but where the shaded region
overlap!
 Your answer is the your graph and shaded region
System of inequalities
 Solve each system of inequalities
3x  4 y  8

 y  5x
System of inequalities
 y  x  4

y   x  2
System of inequality word problem
 Leyla wants to buy fish, chicken, or some of each for
weekend meals. The fish costs $4 per pound and the chicken
costs $3 per pound. She will spend at least $11 but no more
than $15.
 a. Write a system of inequalities
to model the situation.
 b. Graph the system to show the
possible amounts Leyla could buy.
Answer
4x + 3y ≥ 11
4x + 3y ≤ 15
x≥ 0
y≥ 0
Solve a system by matrices
 There are other ways to solve a system besides
graphing. One alternative way is using matrices.
Matrices can be used to solve 2x2 systems and
bigger.
 SOLVE the 3x3 system
2
x

3
y

z


8

2
x

y

z

15



x  9 y  2 z  3


6
x

y

z


11

5 x  6 y  5 z  11
 4x  3 y  z  0


[2nd] , [matrix],  edit, type in systems, [2nd], [quit]
[2nd] , [matrix],  MATH, rref, [A]
The last column is your answer