7.4 Applications of Linear Systems (Pages 396 – 403)

You can solve systems of equations using graphing, substitution, or elimination.

Graphing works best when the y intercept is between -10 and 10, and the slope is a whole number or fraction between -10 and 10.

Substitution works well when you have either an x or y variable with a coefficient of 1 or -1.

Elimination works for any system.

Steps for solving linear systems word problems.

1.  Define your variables-write them our so you and your teachers understand what you mean.

2.  What are we trying to find or relate?

3.  Write your equations.

4.  Choose a method to solve the equations.

5.  Solve.

You have a pocket full of quarters and dimes. You count the number of coins and find you have 45. You find the amount your coins are worth and find you have $5.40. How many dimes and how many quarters do you have?

1.  Define your variables:

Let d = number of dimes, let q = number of quarters

2.  What are we trying to find or relate?

Number of each type of coin Value of $5.40

3.  Write your equations.

d + q = 45 .10d + .25q = 5.40

4.  Choose a method to solve the equations.

I will use elimination. So I will multiply the first equation by -.10.

-.10(d + q = 45) " -.10d + -.10q = -4.50

5.  Solve.

-.10d -.10q = -4.50

.10d + .25q = 5.40 Add equations

.15q = .90 Divide

.15 .15

q = 6

d + q = 45

d + 6 = 45 Subtract 6

-6 -6

d = 39 You have 6 quarters and 39 dimes.

7.5 Linear Inequalities (404 – 410)

Graph as if the inequality is an equation.

Use a dotted or solid line depending on the sign.

(< and > use a dotted line , ≤ and ≥ use a solid line)

Determine which region is included.

y < 2x – 3

y intercept (-3)

slope (21)

dotted line (<)

To determine the region:

Method 1 – Look at the y axis pick which numbers are less than (<)?

-5 is less than -1. So shade BELOW the line.

Method 2 – Try an easy point and see if the inequality is true or false. If it is true shade that region, if false shade the opposite region. [use (0,0) Is 0 < 2(0) – 3 true? 0 is NOT less than -3 so shade the opposite region.

7.6 Systems of Linear Inequalities (411 - 418)

Graph each inequality and its region. Find the overlapping regions—that is your solution.

y ≤ 3x – 2 and y > x + 4

The darkest region on this graph is the solution of the system of inequalities.