Unit 1 solving systems
Download
Report
Transcript Unit 1 solving systems
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