Week 9: Graphing Systems of Inequalities

This week we covered Graphing Systems of Inequalities in the chapter Systems of Equations and Inequalities. 

This is simply review from Algebra from graphing the inequality and shading. 

First you will:

1. Graph each equations

     a line: y=mx+b

     a parabola: y=(x-h)^2 +k

     a circle: x^2 + y^2 = r^2

2. Pick a test point not on the line

3. Shade the plain containing the test point. If the test point satsifies the equation shade the other plane ift id does not

   ≥ or ≤ solid line

   > or < dotted line

This is how you will solve such a problem.

Below is one example of this problem.

In this problem. You can see the equations being graphed and then finding which side to shade. the place where both lines have shaded is the answer for the equation. 

That is how you graph systems of inequalities

See You Next Week!!!

Week 8: Cramer’s Rule

This week’s blog post is on Cramer’s Rule in the lesson Determinants and Cramer’s Rule. This is in the chapter Systems of Equations. 

In this lesson, we reviewed how Determinants worked from last year. Determinants are practically taking two equation like:

x+2y=3

-3x+5y=7

Then they’re put into an equation with Brackets like

_      _

|   1  2  |

| -3  5 |

You then find the determinant by multiplying cross multiply.

then you subtract.

so it would look like

a  b

c  d  

ad-bc

you multiply a times d and then subtract c times b

For Determinents of 3 by 3

It would be

a b c

d e f

g h i

You then draw it again to

a b c a

d e f d

g h i  g

so you multiply just like you did for hte 2 by 2 but by 3. 

To do cramer’s rule you use the determinant to multiply.

You use the originial numbers from the equations but not taking the answers for the equation or the C for the equation. You then find the determinant of that equation. That will be called D

You then replace the first column with the answers in the original equation and then find the determinant. This will be called Dx

You then replace the second column instead with the answers of the original equation. start all over. the answers in the first column would be the original numbers from the original equation. Find the determinant. This will be called Dy.

Do this however many times you need to if there is a third column it will be called Dz.

To Find x: x=Dx/D

To FInd y: y=Dy/D

To FInd z: z=Dz/D

Then the answer will be (x, y, z)

Below is one example of a problem.

That is how you use cramer’s rule.

SEE YOU NEXT WEEK!!!