Systems of two linear equations — Heart of Algebra

Questions in this quiz (7)

1. Solve the system:$$y=2x+3$$$$3x+y=9$$

   • $$(\frac{2}{3},\frac{1}{3})$$
   • $$(\frac{6}{5},\frac{27}{5})$$
   • $$(\frac{1}{2},\frac{3}{2})$$
   • $$(\frac{3}{2},3)$$

2. Solve the system:$$2x+3y=12$$$$4x-3y=6$$

   • $$(4,3)$$
   • $$(3,4)$$
   • $$(4,6)$$
   • $$(3,2)$$

3. A taxi company charges a flat fee of 4 dollars plus 2 dollars per mile. Another company charges a flat fee of 6 dollars plus 1.50 dollars per mile. Find the number of miles for which the two companies charge the same amount.

   • 4
   • 6
   • 8
   • 12

4. At a movie theater, 2 adult tickets and 3 child tickets cost 34 dollars. Three adult tickets and 2 child tickets cost 38 dollars. Find the price, in dollars, of one adult ticket and one child ticket.

   • $$17$$, $$8$$
   • $$17$$, $$11$$
   • $$12$$, $$8$$
   • $$9.2$$, $$5.2$$

5. A student buys 4 pencils and 2 pens for 3 dollars. Another student buys 2 pencils and 3 pens for 2.70 dollars. Find the cost of a pencil and the cost of a pen.

   • $$0.50$$, $$0.75$$
   • $$0.55$$, $$0.70$$
   • $$0.45$$, $$0.60$$
   • $$0.70$$, $$0.50$$

6. The sum of two numbers is 26. Their difference is 6. Find the two numbers.

   • $$10$$ and $$15$$
   • $$16$$ and $$10$$
   • $$12$$ and $$15$$
   • $$9$$ and $$12$$

7. The graph of a system of linear equations is shown. What is the solution $$(x,y)$$ to the system?

   • $$(1,6)$$
   • $$(6,1)$$
   • $$(3,6)$$
   • $$(2,5)$$