Solving systems of Equations & Graphing Linear Inequalities

A bag contains 18 coins consisting of quarters and dimes. The total value of the coins is $2.85. 

Which systems of equations can be used to determine the number of quarters, q, and the number of dimes, d, in the bag?

•  $0.10q+0.25d=2.85$  
   $q+d=18$  
  

•  $0.10q+0.25d=18$  
   $q+d=2.85$  

•  $0.25q+0.10d=2.85$  
   $q+d=18$  
  

•  $0.25q+0.10d=18$  
   $q+d=2.85$  
  

A pizza parlor sells small and large pizzas for to-go orders. One customer orders 2 small pizzas and 3 large pizzas for $60.25. A second customer orders 4 small pizzas and 2 large pizzas for $65.50.

What is the cost of a large pizza?

• $13.75

• $9.50

• $16.38

• $22.25

There are 15 plates in a kitchen cabinet. The diameter of each plate is either 7 inches or 12 inches. The diameter of all 15 plates combined is 140 inches.

Which system of equations can be used to find the number of 7-inch plates, x, and the number of 12-inch plates, y, that are in the cabinet?

•  $x+y=140$  
   $12x+7y=15$  
  

•  $7x+12y=140$  
   $7x+12y=15$  
  

•  $x+y=15$  
   $7x+12y=140$  
  

•  $x+y=15$  
   $12x+7y=140$  
  

Two customers went to a post office to buy postcards and large envelopes. Each postcard costs the same amount, and each large envelope costs the same amount.

 $\circ$  The first customer paid $12 for 14 postcards and 5 large envelopes.
 $\circ$  The second customer paid $24.80 for 10 postcards and 15 large envelopes. 

What was the cost of each large envelope?

• $1.42

• $0.35

• $1.15

• $0.63

What is the y-value of the solution to this system of equations?

  $x=2y-4$  

 $7x+5y=-66$  

•  $-2$  

•  $-\frac{19}{7}$  

•  $-8$  

•  $-\frac{62}{19}$  

Which graph represents the solution set of  $y\ge-\frac{7}{2}x-2$  ?

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Which ordered pair is in the solution set of  $y\ge\frac{1}{3}x+4\$  ?

•  $\left(-6,1\right)$  

•  $\left(-1,6\right)$  

•  $\left(6,-1\right)$  

•  $\left(1,-6\right)$  

Which graph best represents the solution set of  $y>3x-4$  ?

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Which ordered pair is in the solution set of  $8x+16y>32$  ?

•  $\left(0,2\right)$  

•  $\left(-3,5\right)$  

•  $\left(-1,1\right)$  

•  $\left(4,0\right)$  

Which graph best represents the solution set of $-4x\le6y-54$  ?

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