System of Equations — Quiz 1

Questions in this quiz (10)

1. Consider the system of equations:$$-18x + 21y = 54$$$$-9x + 10.5y = -27$$How many solutions does the given system of equations have?

   • Exactly one
   • Exactly two
   • Infinitely many
   • No solution

2. A community consists of a 3-hectare garden and a 40-hectare farming area. The total number of flowers in the community is 4,500. The equation: $$3x + 40y = 4,500$$ represents this situation. Which of the following is the best interpretation of $$x$$ in this context?

   • The average number of flowers per hectare in the garden
   • The average number of flowers per hectare in the farming area
   • The total number of flowers in the garden
   • The total number of flowers in the farming area

3. Sarah and her two cousins have exactly 36 dollars to spend at the carnival. Each ride ticket costs4.00 dollars, and each snack costs 2.00 dollars. If they each want to go on 2 rides, how many snacks can they buy in total?

   • 8
   • 5
   • 6
   • 7

4. If $$x=\frac{5}{3}$$ and $$y=2x+4$$, what is $$3y-6$$?

   • 16
   • $$\frac{22}{3}$$
   • 22
   • $$\frac{16}{3}$$

5. In the system of equations below, what is the value of $$y$$?$$2x+3y=12$$$$5x-y=9$$

   • $$\frac{9}{17}$$
   • $$\frac{42}{17}$$
   • $$\frac{12}{17}$$
   • $$\frac{42}{5}$$

6. A bookstore sells 4 novels for every 5 magazines it sells. If the store sells a total of 180 novels and magazines in a given week, what system of equations could be used to solve for the number of novels $$n$$ and magazines $$m$$ that were sold that week?

   • $$5n = 4m$$ ; $$n + m = 180$$
   • $$n = 4m$$ ; $$n + m = 20$$
   • $$5n = m$$ ; $$n + m = 5$$
   • $$4n = 5m$$ ; $$n + m = 20$$

7. If $$x+2y=6$$ and $$4x-y=17$$ then what is the value of $$x-y$$?

   • $$\frac{10}{4}$$
   • $$\frac{17}{3}$$
   • $$\frac{17}{6}$$
   • $$\frac{11}{3}$$

8. What is the value of $$x$$ in this pair of equations?$$6 - \frac{1}{2}y = x$$ and $$3\left(8 - \frac{5}{4}y\right) = 2x + 4$$

   • $$\frac{5}{2}$$
   • $$\frac{3}{8}$$
   • $$\frac{5}{4}$$
   • $$\frac{50}{11}$$

9. Concert tickets cost $$10$$ for adults and $$6$$ for students. If $$50$$ tickets are sold for a total of $$380$$, how many adult tickets were sold?

   • 80
   • 20
   • 40
   • 30

10. Solve the system:$$12y = -3x + 18$$$$3(x + 4y) = 18$$

    • $$(0,0)$$
    • No solution
    • Only negative values
    • Infinite pair of solutions