Systems of Equations Review

How many solutions?

100

How many solutions does a system of parallel lines have?

0

200

How many solutions does this system have?

{y=3x+4

{y=3x+4

Infinitely many

300

How many solutions does this system have?

{y=1/2x+3

{y=4x+3

One

400

Determine the number of solutions the system has. Justify your answer.

{2y – 4x = 6

{y=2x+3

Infinitely many solutions, because the equations are equivalent.

500

Determine the number of solutions the system has. Justify your answer.

{6x-3y=3

{2x-y=4

Zero solutions. When put in slope-intercept form each equation has the same slope.

Substitution

100

Solve the system of equations using substitution.

{y = -6x – 3

{y = -x + 2

(-1,3)

200

Solve the system of equations using substitution.

{y= 7/4x-3

{y= 4

(4,4)

300

Solve the system by using substitution:

{x= 5-y

{x-2y = 8

(6,-1)

400

Solve the following system by substitution:

{y= -3x+5

{5x-4y = -3

(1,2)

500

Solve using substitution.

{2x+y = 13

{4x-3y = 11

(5,3)

Elimination

100

Solve the following system by using elimination:

{2x+3y = 20

{-2x+y = 4

(1,6)

200

Solve the system using elimination.

{-3x + 2y = 23

{ 5x + 2y = -17

(-5,4)

300

Solve the system by elimination:

{-4x-2y = -12

{ 4x+8y = -24

(6,-6)

400

Solve the system using elimination:

{x+2y = -5

{-5x+2y = 13

(-3,-1)

500

Solve the system of linear equations using elimination.

{7x – 5y = -24

{5y = 9x + 18

(3,9)

Which method is easier?

100

Determine which is the easiest method to use to solve this system. Solve.

{x + y = 7

{x – y = 3

Elimination. (5,2)

200

Determine which is the easiest method to use to solve this system. Solve.

{3x+2y = 6

{y = 1/2x-1

Substitution. (2,0)

300

Determine which is the easiest method to use to solve this system. Solve.

{y = -x + 6

{y= 4/3x-1

Substitution. (3,3)

400

Solve the system of equations and justify your choice of solving method.

{-3x – y = -24

{y – 3x = 30

(-1, 27)

Methods vary.

Elimination, because we can add the equations to eliminate the y terms or subtract the equations to eliminate the x terms.

OR 

Substitution, because it is easy to isolate y in the second equation. 

500

Solve the system of equations and justify your choice of solving method.

{x = y+3

{x = -y-2

(1/2, -5/2)

Methods vary.

Substitution, because they both have the same variable isolated so you can equal them to each other

OR

Elimination, can add the y's to eliminate them and solve for x.

Trivia

100

Which fellow has a color in their name?

Mr. Silverman

200

Which two SAGA workers went to CUNY schools?

Mr. H and Ms. Joseph

300

Which fellow's favorite saying is "Roll Tide"? And what does it mean when we say it during tutorials?

Mr. Thomas. It means either halfway point, 2-minute warning, or start of TTL

400

How many saga workers wear glasses/contacts?

6

500

Which fellow has been to Hawaii?

Mr. Zia