Algebra 2 - Unit 1-3

System of Equations

100

Solve for solution:

7x - 12 = -4y

12 = -4y - x

(4, -4)

200

Solve using Addition Method:

4x + 4y = -8

2x + 9y = -18

(0, -2)

300

Solve using Subtraction method:

7x + 2y = 15

-x - y = 0

(3, -3)

400

Solve by graphing:

y = -4

8x + 2y = -24

(-2, -4)

500

Solve for the system using substitution method:

2(y - x) = 5 + 2x

2(y + x) = 5 - 2y

((-1/2), (3/2))

Slope of a line

100

Write Standard form of the equation:

y + 3 = (-5/4)(x-4)

5x + 4y = 8

200

Find an equation in standard form:

Passing through the points (-4, 8) and (-9, 6)

2x - 5y = -48 

300

Find an equation in standard form:

Through point (5, 1) that is perpendicular to the line x = 4

0x + y = 1

400

Find an equation in standard form:

Through Q(-3, 2) and parallel to the line containing (2, 3) and (1, -2)

5x - y = -17

500

Find the point-slope form of the equation:

through point: (-2, -5)

Perpendicular to: y + (1/3)x = -5

y + 5 = 3(x+2)

Functions

100

Evaluate h(2)

h(a) = a² - (5/4)

(11/4)

200

Evaluate k(1/6):

k(x) = x³ +(1/2)x²

(1/54)

300

g(x) = |x - (1/2)|

Find g(7/4x)

|(7x - 2)/4|

400

f(x) = 4 - x²

g(x) = |2x - 7|

find:

a. f(g(2))

b. g(f(2))

a = -5

b = 7

500

find and simplify f(g(4)):

f(x) = (2x+1)/(x-1)

g(x) = (x+1)/(x-2)

4

Inequalities

100

Find the inequality:

c - 3 > 2c  or  (c/3) > 1

(- inf, -3) (3, inf)

200

Solve:

7 + 5|c| < 1 - 3|c|

no solution

300

(1/2)|d| + 5 > 2|d| - 13

(-12 to 12)

400

DAILY DOUBLE: Solve the proof for double points! If c ≠ 0 and ca = cb then a = b

1. c ≠ 0 and ca = cb

2. (1/c) is a real number

3. (1/c)(ca) = (1/c)(cb)

4. ((1/c) * c)a = ((1/c) * c)b

5. 1 * a = 1 * b

6. ∴ a = b

1. Given

2. Prop of recip

3. mult prop of eq.

4. Assoc prop of mult

5. prop of recip

6. identity prop of mult.

500

Graph:

y + 3 > -6x

y + x < 2

Solution around quadrant 4

dotted lines

Word Problems

100

The smaller of two consecutive even integers is five more than one half of the greater

x = (1/2)(x+2) + 5

200

Jims weekly pay is two thirds of Alicia's. Together they earn $600 per week. What is each person's weekly pay?

A = $360 J = $240

300

Find the measure of the angles of an isosceles triangle if the measure of the vertex angle is 40 less than the sum of the measure of the base angles.

55

400

The cost of printing the school newspaper is $500 for $800 copies and $620 for 1200 copies. If the printing cost is a linear function of the copies printed, find the cost of printing 1500 copies.

$710

500

Fifteen days after Alan began a diet he weighed 176 lb. After 45 days he weighed 170 lb.

a. How much did he weigh at the beginning of the diet?

b. At this rate, when will he weigh 165 lb?

a. 179 lb

b. 165 lb