Systems of Equations

Substitution

100

Is the point (-2, 5) a solution to the equation:

2y + x = 15

No

200

How do you solve a system of equations using substitution? (In other words, if you had to write steps what would they be?)

1. Isolate a variable.

2. Substitute that into the next equation. 

3. Solve for your first variable. 

4. Substitute the value of your first variable in to solve for your second variable.

300

Solve the system using substitution:

x=4y+8

2x+y=-2

(0,-2)

400

Solve the following system using substitution:

6y+x=12

8y-2x=-24

(12,0)

500

Find the solution using substitution:

3x+6y=12

2y=-x-2

No solution

Elimination

100

Is the point (0,6) a solution to the equation:

y = 2x + 6 

Yes

200

How do you solve a system by elimination? (In other words, if you had to write steps to solve systems by elimination what would they be?)

1. Find or make opposite variables.

2. Combine the equations and eliminate one of the variables.

3. Solve for the first variable.

4. Substitute the first variable in to solve for the second variable.

300

Solve the following system using elimination:

y+2x=5

-y-4x=-5

(0,5)

400

Solve the system using elimination:

2x+4y=8

1/4x-4y=10

(8,-2)

500

Find the solution using elimination:

x+7y=7

y=-1/7x+1

Infinitely many solutions

Graphing

100

Name the solution:

(2,-1)

200

Name a solution to the line:

Answers may vary

300

Find the solution to the following system of equations by graphing:

y = 2x + 5

y = -x - 4

(-3,-1)

400

Solve the following system by graphing:

y = 1/2x-4

x = 4

(4,-2)

500

Solve the following system by graphing:

2x+y=8

x+3y=9

(3,2)

Systems Word Problems

100

You and your friend go shopping for school supplies one day. You buy 3 notebooks and 5 pens for $32. Your friend buys 1 notebook and 2 pens for $11. 

3x + 5y = 32

x + 2y = 11

What does x represent and what does y represent?

Let x = notebooks and let y = pens

200

Your school is having a competition to see who can guess how many lollipops are in a jar. The tens digit is 4 more than twice the ones digit. The sum of the digits is 4. 

Write a let statement for your variables. 

Let x = the tens digit

Let y = the ones digit

300

Hats and mittens are on sale! You buy 5 hats and 4 mittens for $30. Your friend buys 3 mittens and 2 hats for $19. 

Write a system of equations to represent this situation. 

Let x = hats

Let y = mittens

5x + 4y = 30

2x + 3y = 19

400

Two families go ice skating. The first family spends $25 on skate rentals for 5 kids and 2 adults. The second family spends $14 on skate rentals for 3 kids and 1 adult. What are the adult and child rental prices? Solve using a system of equations.

Let x = child rentals

Let y = adult rentals

5x + 2y = 25

3x + y = 14

Children cost $3 and adults cost $5.

500

Veronica got 3 times as many stickers as Natalie. Together, Veronica and Natalie got 12 stickers. How many stickers did each of them get? Solve using a system of equations.

Let x = Veronica's stickers

Let y = Natalie's stickers

3y = x

x + y = 12

Veronica got 9 stickers and Natalie got 3.

Mixed Review

100

What kind of slope is pictured?

Negative

200

Solve the equation:

3x + 5 = 23

x = 6

300

Simplify if x = 2, y = 0, and z = -8:

3x + 4y - 2z + 5xz - 2zy

-58

400

Solve the equation:

5x + 6 + x = -3(x + 4)

x = -2

500

Write all rules for adding with integers (positive and negative numbers).

1. Positive + Positive = Positive

2. Negative + Negative = Negative

3a. Positive + Negative = Positive (when |Positive| > |Negative|)

3b. Positive + Negative = Negative (when |Negative| > |Positive|)