System of Equations 1 — Heart of Algebra

Questions in this quiz (10)

1. $$4x+2y=6$$$$x=5-y$$What is the solution $$(x,y)$$ to the system?

   • $$(-2,7)$$
   • $$(2,3)$$
   • $$(3,2)$$
   • $$(-1,4)$$

2. $$3x+4y=22$$$$x+2y=10$$what is the value of $$x+y$$?

   • $$2$$
   • $$3$$
   • $$4$$
   • $$6$$

3. $$x-2y=16$$$$3x-y=7$$what is the value of $$y-x$$?

   • $$-13$$
   • $$-11$$
   • $$2$$
   • $$4$$

4. $$2x+y=x+6$$$$-4x+3y=-6$$If $$(x,y)$$ is a solution to the system, what is the value of$$xy$$?

   • $$\frac{24}{7}$$
   • $$\frac{18}{7}$$
   • $$\frac{18}{49}$$
   • $$\frac{432}{49}$$

5. $$3x-6y=9$$$$x-2y=3$$How many solutions $$(x,y)$$ are there to the system of equations shown above?

   • $$1$$
   • $$2$$
   • Infinitely many solutions
   • No solutions

6. $$y=0.4x+10$$$$x-y=-15$$What is the value of $$y$$?

   • $$\frac{20}{3}$$
   • $$5.3$$
   • $$8.2$$
   • $$-\frac{25}{3}$$

7. $$5x-\frac{1}{2}y=-6$$$$y=3x+14$$What is the solution $$(x,y)$$ to the system?

   • $$(-2,7)$$
   • $$(-1,11)$$
   • $$(4,26)$$
   • $$(\frac{2}{7},\frac{104}{7})$$

8. A local supermarket sells jelly in small, medium, and large jars. Sixteen small jars weigh as much as two medium jars and one large jar. Four small jars and one medium jar have the same weight as one large jar. How many small jars have the weight of one large jar?

   • $$10$$
   • $$9$$
   • $$8$$
   • $$7$$

9. On a science quiz with $$25$$ questions, $$4$$ points are awarded for each correct answer and $$1$$ point is deducted for each incorrect answer. Maria answered all the questions and earned a total score of $$79$$ points. Which of the following systems of equations represents Maria’s number of correct answers, $$x$$, and incorrect answers, $$y$$?

   • $$x+y=79$$ $$4x-y=25$$
   • $$x+y=25$$$$4x-y=79$$
   • $$x+y=25$$$$x-4y=79$$
   • $$x+y=79$$$$4x+y=25$$

10. A banquet hall has two types of tables. Square tables seat $$6$$ people each, and round tables seat $$10$$ people each. There are $$28$$ tables total, and the tables can seat $$216$$ people altogether. How many square tables are in the banquet hall?

    • $$4$$
    • $$8$$
    • $$16$$
    • $$64$$