Ch. 5 Systems and Matrices

Solving systems(5.1)

100

Solve using substitution: 

a) 4x+3y=-13

b)        y=x+5

(-4,1)

200

Solve using substitution:

a) 3x+4y=4

b) x-y=13

(8,-5)

300

Solve using elimination (the addition method):

a) 3x-7y=15

b) 3x+7y=15

(5,0)

400

Solve using elimination:

a) 9x-5y=1

b) -18x+10y=1

No solution

(answer: 0=3)

500

What is the ordered pair called that we find. 

Mrs. B and the textbook refer to this ordered pair as the solution to the system. But what is this solution? 

The solution is called the "Point of Intersection"

Matrices, Determinants and Cramer's Rule(5.2 & 5.3)

100

Find the value of the determinant: 

-4  -3

 7   4

Determinant = 5

200

Solve using Gaussian Elimination:

3x+6y=9

-4x+y=33

(-7,5)

300

Write the system of equations associated with the augmented matrix:

1 1 0 2

0 4 1 -5

1 0 -1 8

x+y=2

4y+z=-5

x-z=8

400

Use Cramer's Rule to solve:

x+y=6

x-y=2

(4,2)

500

Solve the equation for x:

6x x      =25

25 x      

(-5/6,5)

Partial Fractions and Systems on Nonlinear equations(5.4 & 5.5)

100

Without solving, how would we split up (set up) this partial fraction decomposition:

(9x+29)/(x^2+7x+12)

Factor denominator first: (x+3)(x+4)

then would be:

(9x+29)/(x+3)(x+4)=A/(x+3)+B/(x+4)

200

Without solving, how would we set up this partial fraction decomposition:

(5x+4)/(x+2)^3

(5x+4)/(x+2)^3=A/(x+2)+B(x+2)^2+C/(x+2)^3

300

Identify the graph of each:

1. x+y=5

2. x^2+y^2=9

3. y=2x^2

1. Line

2. Circle

3. Parabola

400

Solve:

x^2=y-1

y=3x+5

(4,17),(-1,2)

500

How many solutions can a circle have?

Circles can have 0, 1, or 2 solutions

Systems of inequalities(5.6)

100

Identify the graphs:

1. x+y=24

2. x^2+y^2=100

1. Line

2. Circle

200

Identify the graphs:

1. y=x

2. y-2x=6

3. y=x^2+10

4. x=-y^2

1.Line

2. Line

3. parabola

4. Parabola

300

How should we draw the lines for this graph?

x+y<4

x-2y>6

Both the lines should be dashed

400

Identify the type of graph and if the line should be dashed or solid:

1. x^2+y^2<4

2. y<_ x    (y is greater than or equal to x)

1. Circle and dashed line

2. Line and solid line

500

What is the shortcut method to find out where to shade the graph at?

The shortcut method:

if y is (+) > shades above and < shades below

if y is (-) > shades below and < shades above

Properties of Matrices(5.7)

100

Find w, x, y & z:

|-7 x|= |w -4|

|y -2|   |-2  z|

w= -7

x= -4

y= -2

z= -2

200

Find A + B:

|-3 9|+ | 8  2|

|-5 0|   |-4 10|

|5  11|

|-9 10|

300

Find 4A:

4 | -3  9|

   |  -5 0|

|-12 36|

|-20   0|

400

Find A*B:

|-3 9|*|8    2|

|-5 0|  |-4 10|

|-60 84|

|-40 -10|

500

Solve:

|5 6|*|1 0|

|8 9|  |0 1|

|5 6|

|8 9|