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February 4, 2014

Today:
 Review for test and systems
of equations < 20 min
 Test: Inequalities & Lines
Notes:
new people—take the test, do the best you can Write
your name on front for now. codes to come
Alt.Khan from last week (inequalities) is here. Due
on or before next Monday feb. 10
On-line Khan: You can finish last week’s topics by
this Sunday for full credit.
Pencil only for test, ask if you are not sure of your
code.
Take 3 minutes to get ready, clear your desk except
for scratch paper.
Inequalities
24x + 2y < - 3
y > -x
y< 4
x<3
Parallel & Perpendicular Lines

The equations of two lines are given.
Determine the number of solutions.

A) None B) One C) Two D) Three

E) Infinite

Since the lines are not parallel (none), nor are they the
same line (infinite), they will, at some point cross. The
answer is..
Review: Systems of Equations (3)
Solve the systems of equations by graphing

1 =

1+0

2 +

( + 0)
1 = 3

(2,1)

Step 1: Put both equations in
slope - intercept form.

Step 2: Graph both equations on
the same coordinate plane.

Step 3: Plot the point where the
graphs intersect.

Step 4: Check to make sure your
solution makes both equations true.
Review: Systems of Equations (3)
Solve the systems of equations by elimination

 Elimination is easiest when the equations
are in standard form.
1: Put the equations in
Standard Form.
Step 2: Determine which

variable to eliminate.
Step 3: Add or subtract

the equations.
Step 4: Plug back in to

find the other variable.
Step 5: Check your

solution.

Standard Form: Ax + By = C
Look for variables that have
the same coefficient.
Solve for the variable.
Substitute the value of the
variable into the equation.
Substitute your ordered pair
into BOTH equations.
Review: Systems of Equations (2)

2x + 7y = 31
5x - 7y = - 45

7x + 0 = -14

x = -2

Like variables must be lined under each other.

THEN----
Review: Systems of Equations (2)

2X + 7Y = 31
2(-2) + 7y = 31
-4 + 7y = 31
Substitute your
4
4
answer into either
original equation
and solve for the
second variable.

7y = 35; y = 5

Solution

(-2, 5)

Now check our answers in both equations---
Review: Systems of Equations (2)

2x + 7y = 31
2(-2) + 7(5) = 31
-4 + 35 = 31
31 = 31
5x – 7y = - 45
5(-2) - 7(5) = - 45

-10 - 35 = - 45
- 45 =- 45
Review: Systems of Equations (1)
And Finally.....
A shopper bought two pairs of gloves and four hats
for $43.00. Her friend bought two pairs of gloves and
two hats for $30.00. What is the price of each item?
Use ‘g’ for gloves and ‘h’ for hats.
Equation 1:
Equation 2:

2g + 4h = $42.00

2g + 2h = $30.00

Hats are $6.00 each

Plug both values in
0g + 2h = $12.00
and check for
2g + 24 = $42.00
equality.
2g = $18.00; g = $9
Feb. 4, 2014

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Feb. 4, 2014

  • 1. February 4, 2014 Today:  Review for test and systems of equations < 20 min  Test: Inequalities & Lines
  • 2. Notes: new people—take the test, do the best you can Write your name on front for now. codes to come Alt.Khan from last week (inequalities) is here. Due on or before next Monday feb. 10 On-line Khan: You can finish last week’s topics by this Sunday for full credit. Pencil only for test, ask if you are not sure of your code. Take 3 minutes to get ready, clear your desk except for scratch paper.
  • 3. Inequalities 24x + 2y < - 3 y > -x y< 4 x<3
  • 4. Parallel & Perpendicular Lines The equations of two lines are given. Determine the number of solutions. A) None B) One C) Two D) Three E) Infinite Since the lines are not parallel (none), nor are they the same line (infinite), they will, at some point cross. The answer is..
  • 5. Review: Systems of Equations (3) Solve the systems of equations by graphing 1 = 1+0 2 + ( + 0) 1 = 3 (2,1) Step 1: Put both equations in slope - intercept form. Step 2: Graph both equations on the same coordinate plane. Step 3: Plot the point where the graphs intersect. Step 4: Check to make sure your solution makes both equations true.
  • 6. Review: Systems of Equations (3) Solve the systems of equations by elimination  Elimination is easiest when the equations are in standard form. 1: Put the equations in Standard Form. Step 2: Determine which variable to eliminate. Step 3: Add or subtract the equations. Step 4: Plug back in to find the other variable. Step 5: Check your solution. Standard Form: Ax + By = C Look for variables that have the same coefficient. Solve for the variable. Substitute the value of the variable into the equation. Substitute your ordered pair into BOTH equations.
  • 7. Review: Systems of Equations (2) 2x + 7y = 31 5x - 7y = - 45 7x + 0 = -14 x = -2 Like variables must be lined under each other. THEN----
  • 8. Review: Systems of Equations (2) 2X + 7Y = 31 2(-2) + 7y = 31 -4 + 7y = 31 Substitute your 4 4 answer into either original equation and solve for the second variable. 7y = 35; y = 5 Solution (-2, 5) Now check our answers in both equations---
  • 9. Review: Systems of Equations (2) 2x + 7y = 31 2(-2) + 7(5) = 31 -4 + 35 = 31 31 = 31 5x – 7y = - 45 5(-2) - 7(5) = - 45 -10 - 35 = - 45 - 45 =- 45
  • 10. Review: Systems of Equations (1) And Finally..... A shopper bought two pairs of gloves and four hats for $43.00. Her friend bought two pairs of gloves and two hats for $30.00. What is the price of each item? Use ‘g’ for gloves and ‘h’ for hats. Equation 1: Equation 2: 2g + 4h = $42.00 2g + 2h = $30.00 Hats are $6.00 each Plug both values in 0g + 2h = $12.00 and check for 2g + 24 = $42.00 equality. 2g = $18.00; g = $9