Unit+1

=Unit 1 - Using Linear Systems to Solve Problems=

Unit 1 - Overview
>
 * Solve two linear equations by graphing. The solution is the point of intersection
 * Know the three difference ways two lines can intersect
 * Model Word Problems using linear equations
 * Solve linear system by substitution
 * Solve linear system by elimination
 * Solve linear system using Graphing calculator
 * Solve Word Problems.
 * Unit 1 - Rubric

1.1 Solving Linear System by Graphing
Graphing is great to visualize the problem, and it is helpful use sketches to help verify algebraic answers. However they are time consuming, and can be less accurate than solving algebraically. Use a table of values. You will need to do this in the quadratics unit, and better to get used to that now.

p. 60-62 #(1-9) even letters, 11, 16

1.2 Solving Linear Systems by Substitution
Lesson 2 - Solving by Substitution

Graphing sometimes does not give exact solutions, so we use algebraic methods.

To solve a linear system by substitution 1. Put equations in ax + by = c form 2. Choose one of the equations and isolate one it's variables. 3. Substitute the expression that you have, into the other equation. 4. Solve the new equation (it will only have one variable) 5. Substitute the value you calculated into one of the original equations. 6. Verify that the ordered pair works in both original equations.

For step 1, always look for a variable that is easy to solve for.

HW: p. 92 # 1ad, 2ad, 4ac, 7abd, 8abde, 12abcd.

Day 2 - Do the rest of question 12. Try some enrichment problems in 'C' section.

1.3 Using Elimination
To solve a linear system by elimination 1. Express both equations in the form ax + by = c 2. Choose a variable to eliminate, then multiple one or both equation by a number so the co-efficients of one variable are the same (or opposite). 3. Subtract (or add) the two equations. (Note that adding is easier, so opposite signs are preferred) 4. Solve the remainding equation (only one variable). 5. Substitute the value you calculated into one of the original equations. 6. Verify that the ordered pair works in both original equations.

Elimination is often easier than substitution. Normal you only use substitution if one variable has a co-efficient of 1, and therefore is easy to isolate.


 * HW. Page 101 all of #2, #3, #6(every second one), both sides of worksheet**

**1.4 Investigating the Ways that Two Lines Can Intersect**

 * type of solution ||  || slope || y-intercept ||
 * one solution || lines are not parallel || different ||  ||
 * no solutions || lines are parallel, different y-intercept || same || different ||
 * infinite number of solutions || lines are parallel with same y-intercept || same || same ||

HW: p. 69 # 3, 5, 7, 10, 12

1.5 Modeling with Linear Equations
Types of problems: 1. Relationship between numbers 2. Time-Speed-Distance 3. Interest Rates / Chemical Solutions 4. Mixture Problems 5. Geometry Problems 6. Money Problems HW: -p. 50 # 2

-write a system of equations for each of the following, but DO NOT SOLVE:
 * 11, 14, 19, 21, 23, 25, 28, 33.

-do p. 53 # 30, too.

1.6 Geometry Problems
Remember Geometry theorems. 1. The interior angles of a triangles add up to 180 degrees 2. Supplementary Angles add up to 180. 3. Opposite Angels are equal 4. Parallel Lines Theorems.
 * Alternative Angles are Equal
 * Corresponding Angles are Equal
 * Co-Interior Angles add up to 180

Work: pg. 94 #21 (10 mins) this is homework!

Review work for practice this weekend: Pg. 121 #4, 5 Pg. 123 # 6, 8, 9 Pg. 128 #16, 17 (tough), 19, 20 Pg. 131 # 21, 22 (tough) 23, 24 Try the review Test on page 137 too if you want the extra practice

1.7 Using the Graphing Calculator
1. Find x and y-intercepts by zooming in and using TRACE 2. Find point of intersection using CALC - 5. Intersection function 3. Do some linear regression questions

Note that linear regression will not be on test. As well, no questions specific to the calculator will be on test. Notes on your calculator questions will be marked.