Heart of Algebra: Systems of Equations — Quiz 2

Questions in this quiz (10)

1. A school sells notebooks for $$3$$ dollars each and folders for $$2$$ dollars each. A student buys $$10$$ items for a total of $$24$$ dollars. How many notebooks did the student buy?

   • $$4$$
   • $$6$$
   • $$8$$
   • $$10$$

2. Which system of linear equations has no solution?

   • $$3x+2y=5,\ 6x+4y=10$$
   • $$3x+2y=5,\ 6x+4y=12$$
   • $$3x+2y=5,\ 2x-y=1$$
   • $$x+y=4,\ 2x+2y=8$$

3. In June, a store sold $$20$$ more than twice the number of items it sold in July. In total, the store sold $$260$$ items in June and July. How many items did the store sell in July?

   • 80

4. $$-x-wy=-205$$$$3x-wy=35$$The solution to the system is $$(x,y)$$ and the graphs intersect at a point where $$y=10$$. What is the value of $$w$$?

   • 14.5

5. A concert sells adult tickets for $$15$$ dollars and student tickets for $$9$$ dollars. A total of $$40$$ tickets were sold for $$480$$ dollars. How much money, in dollars, was collected from adult tickets?

   • 300

6. $$5x+2y=4$$$$15x+6y=12$$For each real number $$x$$, which of the following points lies on the graph of both equations?

   • $$(x,-\frac{5}{2}x+2)$$
   • $$(x,-\frac{5}{2}x+4)$$
   • $$(x,\frac{5}{2}x+2)$$
   • $$(x,\frac{5}{2}x+4)$$

7. A theme park sells regular tickets for $$20$$ dollars and VIP tickets for $$50$$ dollars. On a certain day, $$100$$ tickets were sold for a total of $$2,900$$ dollars. Which system of equations represents this situation, where $$r$$ is regular tickets and $$v$$ is VIP tickets?

   • $$r+v=100,\ 20r+50v=2900$$
   • $$r+v=2900,\ 20r+50v=100$$
   • $$20r+50v=100,\ r+v=2900$$
   • $$50r+20v=2900,\ r+v=100$$

8. A rope of length $$40$$ inches is cut into two pieces. One piece has length $$x$$, and the other has length $$y$$. The value of $$x$$ is $$5$$ more than twice the value of $$y$$. What is the value of $$x$$?

   • 85/3

9. $$\frac{3}{4}x+\frac{5}{4}y=6$$$$gx+ky=12$$The system has infinitely many solutions. What is the value of $$\frac{g}{k}$$?

   • 3/5

10. $$\frac{3}{2}x+4y=20$$$$\frac{1}{2}x+4y=12$$If $$(x,y)$$ is the solution, what is the value of $$3x+8y$$?

    • $$12$$
    • $$24$$
    • $$36$$
    • $$40$$