Algebra 2 test 1 prep.

Solving systems of equations in 2 variables

100

This method can be used to remove one variable from a system by adding the system components together.

Elimination method. 

200

This method uses the Slope intercept form to remove the "y" variable from a system. 

Substitution method. 

300

Solve the Following System of equations:
2x+3y=-3
x+2y=2

(-12,7)?

400

Solve the Following System of equations:

7x + 2y = –1
4x – 3y = –13

(–1, 3)

500

Solve the Following System of equations:

4x-y=6
2x-y/2=4

no solution

Solving systems of inequalities by graphing

100

What is the answer to this type of question?

the area that the shaded regions of each inequality cross over.

200

the 3 main steps to solving systems of inequalities

Graph, Plug in (0,0), shade

300

Solve the system of inequalities
y ≤ 2x – 3
y ≤ – 1/2x + 2

SEE OTHER SHEET

400

Solve the system of inequalities
3y > 4x
2x – 3y > –6

See other page

500

Solve the system of inequalites:

IyI ≤ 1
y < x – 1

See other page

Solving systems of equations in 3 variables

100

What methods can be used to solve a system in 3 variables?

Elimination and Substitution method

200

Solve each system of equations:
x – 4y + 3z = –27
2x + 2y – 3z = 22
4z = –16

(1, 4, –4)

300

Solve this system of equations. 
2x – y + 2z = 15
–x + y + z = 3
3x – y + 2z = 18  

(3, 1, 5)

400

Solve the System of equations.

3m – 2n + 4p = 15
m – n + p = 3
m + 4n – 5p = 0  

(3, 3, 3)

500

Solve the system.
2x + 3y + 4z = 2
5x – 2y + 3z = 0
x – 5y – 2z = –4

(2, 2, –2)

Solving system of inequalities for vertices

100

How many problems are involved in solving for the verticies?

3 

200

What does the greater or less than signs become in these problems?

an equal sign

300

Solve for the verticies:
y ≥ 1 – x
y ≤ x – 1
x ≤ 3

(1, 0), (3, 2), (3, –2)

400

x – y ≤ 2
x + y ≤ 2
x ≥ –2

(–2, 4), (–2, –4), (2, 0)

500

y ≥ 2x – 2
2x + 3y ≥ 6
y < 4

(–3, 4), ( 𝟑/𝟐 , 𝟏), (3, 4)

Brain Teasers

100

Multiply this number with any other number and you will always get the same answer. What’s the number?

0

200

One grandmother, two mothers, and two daughters went on a trip to the zoo together and bought one ticket each. How many tickets did they buy

The answer is three. The grandmother is also a mother and the mother is also a daughter.

300

What 5-letter word becomes shorter when you add two letters to it?

Short

400

The butcher is 5ft 11 inches tall and he has size 9 feet. What does he weigh?

Meat

500

There is a clothing store where the owner has come up with his own method of pricing his items. A tie costs $15, a shirt costs $25, a skirt costs $25, and trousers costs $40. Using this method, how much would a coat cost?

The answer is $20. The method is adding $5 for each letter in the name of the item.