Systems of Equations & Inequalities

Solve the systems of equations by graphing:

 $x+y=2$  

 $x-y=4$  

• (3, -1)

• (1, -3)

• (-1, 3)

• (-3, -1)

Solve the system of equations by substitution: 

 $6x-y=-21$  
 $5x+3y=17$  

• (-2, 9)

• (-2, 5)

• (2, -9)

• Infinite Solution

• No Solution

Solve the systems of equations by elimination:

 $2x+8y=6$ 
 $5x+20y=15$  

• Infinite Solution

• (0, 5)

• No Solution

• (1, 5)

• (2, -5)

Jim sells hot dogs for $2.95 each and steak sandwiches for $9.95 each out of his food cart. During an outdoor festival, he sold a total 985 items for $7343.75. How many steak sandwiches did he sell?

• 634

• 351

• 590

• 272

Graph the linear equality below. Select the coordinate that would be in the shaded region.

 $2x-3y<6$  

• (8, -7)

• (-1, -10)

• (1, 5)

• (0, -9)

Graph the systems of inequalities below. Select the coordinate that would be in the shaded region.

 $y<3x-2$   
 $y>-x+3$  

• (5, 2)

• (0, 7)

• (1, -8)

• (-2, 2)

A theater has a maximum capacity of 1,000 people. For their latest production, adult tickets costs $25 and child tickets are $12.50. The theater must make at least $15,000.

Pick two options are possible solutions.

• 700 adult, 100 child

• 400 adult, 500 child

• 500 adult, 100 child

• 700 adult, 400 child