QUESTIONS
Question 1
Enrique is making a party mix that contains raisins and nuts. For each ounce of nuts, he uses twice the amount of raisins. How many ounces of nuts and how many ounces of raisins does he need to make 24 ounces of party mix?
Use the graph to solve the system of equations you develop, then enter your solution below.
Question 2
Solve the system by graphing:
{y = 7X/2 + 9
{−2x+y=6
(Plot both lines and the point of intersection by moving the dots to the correct location.)
Question 3
Owen is making lemonade from concentrate. The number of quarts of water he needs is 4 times the number of quarts of concentrate. How many quarts of water and how many quarts of concentrate does Owen need to make 100 quarts of lemonade?
Question 4
Owen is making lemonade from concentrate. The number of quarts of water he needs is 4 times the number of quarts of concentrate. He wants to make 100 quarts of lemonade.
Let c represent the number of quarts of concentrate, and let w represent the number of quarts of water Owen will use. Which of the following systems of equations models this situation?
{c = 4w, w+100 = c
{c=4w, w+c=100
{w=4c, 100+c=w
{w=4c, w+c=100
Question 5
Use the graph to solve the given system of equations by plotting both lines and the point of intersection by moving the dots to the correct location, then enter your solution below.
{y= 3x – 9
{-x +y =-3
Question 6
Determine which of the following ordered pairs satisfies the given system of equations.
{10x−6y=9
{−x−2y=3
- (−2, -29/6)
- (0, -3/2)
- (2/5, −1)
- (3, −3)
- (−5, 4)
Question 7
Determine which of the following ordered pairs satisfies the given system of equations.
{−2x+y=8
{y=2×5−8
(7/2, −7/2)
(−3, 2)
(−1, 5)
(−2, −44/5)
(−10, −12)
Question 8
Without graphing, determine the number of solutions to the system of equations.
{6x−4y=9
{12x−8y=18
- no solution
- one solution
- infinitely many solutions
Question 9
Without graphing, determine the number of solutions to the system of equations.
{−9x+5y=10
{36x/5−4y = 4
- no solution
- one solution
- infinitely many solutions
Question 10
Does the ordered pair (2/3, −5/6) satisfy the following system of equations?
{−8x−10y=3
{6x−6y=9
- yes
- no
Question 11
Determine which of the following ordered pairs satisfies the given system of equations.
{−6x−6y=4
{y=x−3
- (-3/7, 1/2)
- (0, 0)
- (−3, 7/3)
- (7/6, 11/6)
- (0, −3)
Question 12
Solve the system by graphing:
{y= -7x/2+9
{2x−y=2
(Plot both lines and the point of intersection by moving the dots to the correct location.)
Question 13
Use the graph to solve the given system of equations by plotting both lines and the point of intersection by moving the dots to the correct location, then enter your solution below.
{y= −4x−12
{y=−3x−8
Question 14
Without graphing, determine the number of solutions to the system of equations.
{2x−10y =−2
{y= x/5−1
- no solution
- one solution
- infinitely many solutions
Question 15
Without graphing, classify the system of equations as either independent or dependent.
{4x−y= −9
{28x−7y= −63
- independent
- dependent
Question 16
Eli is making a party mix that contains pretzels and chex. For each cup of pretzels, he uses 3 cups of chex. How many cups of pretzels and how many cups of chex does he need to make 12 cups of party mix?
Question 17
Eli is making a party mix that contains pretzels and chex. For each cup of pretzels, he uses 3 cups of chex. He wants to make 12 cups of party mix.
Let p represent the number of cups of pretzels, and let c represent the number of cups of chex used. Which of the following systems of equations models this situation?
- {c=3p, p+c=12
- {p=3c, p+c=12
- {p=3c, p−c=12
- {c=3p, p+12=c
ANSWERS:
Question 1
Enrique is making a party mix that contains raisins and nuts. For each ounce of nuts, he uses twice the amount of raisins. How many ounces of nuts and how many ounces of raisins does he need to make 24 ounces of party mix?
Use the graph to solve the system of equations you develop, then enter your solution below.
Answer: 8 ounces, raisins: 16 ounces
Question 2
Solve the system by graphing:
{y = 7X/2 + 9
{−2x+y=6
(Plot both lines and the point of intersection by moving the dots to the correct location.)
Answer:
Question 3
Owen is making lemonade from concentrate. The number of quarts of water he needs is 4 times the number of quarts of concentrate. How many quarts of water and how many quarts of concentrate does Owen need to make 100 quarts of lemonade?
Answer: concentrate: 20 quarts, water: 80 quarts
Question 4….
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