Systems Study Guide

Systems Study Guide

By Kimberlee Joy

1. manipulate equation to be in y= or x=

2. substitute

3. distribute/CLT/solve

4. don't forget to find other variable​

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​Solve by Substitution

Multiple Choice

Solve the system by substitution.  

5x + 4y= −14

7x + y =   −  15 

• (-2, -1)
• (1, -2)
• (-2, 1)
• (-1, -2)

1. use a multiplier to create opposite terms

2. add equations and solve for variable

3. don't forget to find other variable​

​Solve by Elimination

Multiple Choice

Solve the system by elimination.

−6x + 6y = 0

9x − 8y = 4

• (4, −9)

• Infinite number of solutions

• (−9, 4)

• (4, 4)

Slope Intercept

y=-3/4x+2

plot y-intercept

use slope to get points

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Standard Form​

6x-4y=-24

find the x and y intercepts​

​Solve by Graphing

Multiple Choice

Solve this system of equations by graphing.

-x + 2y = 4

y = -3x + 9

• (2, 3)

• (-2, -3)

• (3, 2)

• (-3, 2)

2 coffees and 2 donuts cost $12

1 coffee and 2 donuts cost $7​

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​Word Problems

​Generic Total

Money Total​

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Multiple Choice

Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

• 4x + 6y = 3
  13.5x - 13y = 6
• x + y = 4
  x - y = 6
• 4x + 6y = 13
  3x + 7y = 13.5
• 4x - 6y = 13
  3x - 7y = 13.5

Multiple Choice

The senior class at Rivermont High School rented and filled 11 vans and 3 buses with 283 students. The senior class at Washington High School rented and filled 12 vans and 14 buses with 770 students. Which system of equations solves this problem to show how many students were in each van and each bus?

• 11v + 3b = 283

  12v + 14b = 770

• v + b = 14

  v + b = 16

• 11v + 12v = 283

  3b + 14b = 770

• v + b = 30

  23v + 17b = 1053

Multiple Choice

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740
• S + A = 530
  4S + 3A = 1740
• S + A = 1740
  3S + 4A = 530
• S + A = 1740
  4S + 3A = 530