Math Minutes

•Pick up a study guide as you come in.

•Complete #26-29 only in the Math Minutes packet. DO NOT GO ON!!!.

•Finished? Work on TCAP Mastery. It’s due tomorrow! If you would like it checked, have it out on your desk.

Must show work on both to receive credit!!!

Most Missed Test Questions

Tamara read a newspaper article about the cost of attending a university in 2005.

• The average cost to attend a public university was about $12,000 per year.

• The average cost to attend a private university was about $30,000 per year.

• The author of the article stated that a person would save between $40,000 and $50,000 over 4 years by attending a public university.

Which statement best describes the author’s statement?

A. It is valid because the total cost over 4 years of attending both types of universities is about $42,000.

B. It is invalid because the total cost over 4 years of attending both types of universities is about $168,000.

C. It is invalid because the difference in costs over 4 years of attending a private university to a public university is about $18,000.

D. It is invalid because the difference in costs over 4 years of attending a private university to a public university is about $72,000.

***Most chosen incorrect answer was C***

Most Missed Test Questions

***Most chosen incorrect answer was C***

Why is “C” incorrect?The diagram below shows the location of two schools on a map.

The length of each grid square represents one mile.

• One route requires traveling northeast on Lookout Road.

• One route requires traveling east on Broadway and north on Main Street.

What is the approximate difference between these routes?

Lookout Road

Broadway = 16 miles

Main Street = 11 miles

A.7.6 miles

B.11.0 miles

C.19.4 miles

D.27.0 miles

Mrs. Manley

Systems of Equations

How do you find solutions to systems of two linear equations in 2 variables?

Lesson Objective

❖ Use the substitution method to solve a system of linear equations

A solution of such a system is an ordered pair which is a solution of each equation in the system.

Example: The ordered pair (4, 1) is a solution of the system since

3(4) + 2(1) = 14 and 2(4) – 5(1) = 3.

A set of linear equations in two variables is called a system of linear equations.

3x + 2y = 14

2x + 5y = 3

Example: The ordered pair (0, 7) is not a solution of the system

since

3(0) + 2(7) = 14 but 2(0) – 5(7) = – 35, not 3.

A system of equations with at least one solution is consistent. A system with no solutions is inconsistent.

Systems of linear equations in two variables have either no solutions, one solution, or infinitely many solutions.

y

x

infinitely many solutions

y

x

no solutions

y

x

unique solution

Substitution Method

1. Choose one equation and solve for y (choose the easiest). In other words, change the equation to slope- intercept form - y = mx + b.

2. Substitute the expression that equals y into the remaining equation for the y variable.

3. Solve for x.

4. Now, substitute the value found for x back into either of the original equations.

5. Solve for y.

6. Write your solution as a coordinate pair (x,y).

7. Check your solution (x,y) to be sure it works in both the original equations.

Slope-Intercept Formy = mx + by = mx + b

y = x - 2

y = -x - 4

Examples

Y = 4x + 3Y = x

Examples

y = -2x + 10y = x + 1

Examples

y -1/4x + 5y = x + 2

Examples

y = x + 1y = -4x + 10

y = mx + bax + by = c

y = 2x - 7

-3x + 6y =12

Examples

3x + 5y = 10y = x + 2

Examples

-2x + y = 6y = -4x - 12

Examples

3x + 4y = 11y = 2x

Examples

-4x + 8y = 12y = -12x + 64

Standard Formax + by = cax + by =c

3x + y = 2

x - 2y = 10

Examples

-3x + 5y = 102x + ½y = 24

Examples

-2x + 1/3y = 76x – 1/5y = -9

Examples

7x – 2y = -13x – 2y = 11

Examples

-4x + y = 6-5x – y = 21

Example 1

3x + 2y = -1x - y = 3

Example 2

4x + 6y = 126x + 9y = 36

Example 3

4x + 5y = 32x - 3y = 7

Example 42x + y = 34x + 2y = 5