Systems of Equations

Eliezer's Ice Cream Shop sells sundaes (x) for $2 and banana splits (y) for $3. On a hot summer day, he sold 8 more sundaes than banana splits and made $156.

• x = y + 8

  3x + 2y = 156

• y = x + 8

  2x + 3y = 156

• x = 8y

  2x + 3y = 156

• x = y + 8

  2x + 3y = 156

Tags

CCSS.8.EE.C.8C

What would be the first step in finding the solution using elimination?

2x+ 2y = -2

3x - 2y = 12

• You cannot solve this using elimination.

• Add the two equations to eliminate the y variable.

• Subtract the two equations.

• Multiply the top equation by 3 and the bottom equation by 2.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Yenca’s Yacht Club Hotel is offering two vacation specials. One special includes a 2-night stay with 3 meals and costs $195. The other includes a 3-night stay with 5 meals and costs $300. If the cost per meal is the same in both deals, what is the cost of a single meal?

• $20

• $15

• $75

Tags

CCSS.8.EE.C.7B

The length (y) of a rectangle is equal to triple the width (x). The perimeter of the rectangle is 86 centimeters. Which system models this situation?

• y = 3x

  2x + 2y = 86

• y = 3x

  x + y = 86

• x = 3y

  2x + 2y = 86

• x = 3y

  xy = 86

Answer explanation

triple means times 3!

Tags

CCSS.8.EE.C.8C

What is the solution to this system of equations?

7x - y = 10

-7x + y = -14

• No solution

• Infinitely many solutions

• (4, 1)

• ((2, -4

Answer explanation

These are parallel lines

Tags

CCSS.8.EE.C.8B

When the solution to a system of equations is infinitely many, what will its graph look like?

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Answer explanation

The equations are the same!

Tags

CCSS.8.EE.C.8A

Alex decides to order fast food delivery. If her orders from McDonalds, each sandwich costs $3.50 and there is a delivery fee of $8. If he orders from KFC, each sandwich costs $5.5O but the delivery fee is only $2. How many sandwiches does he have to order for the cost to be the same from each restaurant?

• 3

• 2

• 4

• 5

Wyatt is a high school basketball player. In a particular game, he made some three point shots (x) and some two point shots (y). Wyatt made a total of 12 shots altogether and scored a total of 32 points. Determine the number of two point shots Wyatt made.

• 8 two-point shots

• 4 tow-point shots

• 6 two point shots

Tags

CCSS.8.EE.C.8C

What is the solution to this system of equations?

• (1, 4)

• (0.-4)

• (0, 2)

• (4, 1)

Tags

CCSS.8.EE.C.8B

Match the system of linear equations to the corresponding graph.

 $y\ =\ 2x\ -5$  
 $y\ =\ -\ \frac{3}{2}x+2$  

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Tags

CCSS.8.EE.C.8B