Heart of Algebra: Systems of Equations — Quiz 1

Questions in this quiz (10)

1. $$y=3x+2$$$$3y=12x-6$$What is the value of $$x-y$$?

   • -10

2. $$18x+y=30$$$$6x+y=6$$What is the value of $$y$$?

   • -6

3. At how many points do the graphs of the equations $$y=2x+5$$ and $$y=2x-3$$ intersect in the $$xy$$-plane?

   • $$0$$
   • $$1$$
   • $$2$$
   • $$\text{Infinitely many}$$

4. A mixture has a total mass of $$40$$ grams and is $$25\%$$ salt. It is formed by combining two solutions: one is $$10\%$$ salt and the other is $$50\%$$ salt. What is the mass, in grams, of salt from the $$50\%$$ solution?

   • $$5$$
   • $$7.5$$
   • $$10$$
   • $$12$$

5. $$(x+4)-3(y-2)=20$$$$(x+4)+3(y-2)=44$$The solution to the system is $$(x,y)$$. What is the value of $$3(x+4)$$?

   • 96

6. $$y=5x-1$$One of the two equations in a system is given above. The system has infinitely many solutions. Which equation could be the second equation?

   • $$y=5x+1$$
   • $$2y=10x-2$$
   • $$y=-5x+1$$
   • $$2y=10x+2$$

7. $$x=-2$$$$y=4x+1$$Which of the following points $$(x,y)$$ is the solution?

   • $$(-2,-7)$$
   • $$(-2,9)$$
   • $$(2,-7)$$
   • $$(2,9)$$

8. $$5x-3y=7$$$$2x+6y=8$$If $$(x,y)$$ is the solution, what is the value of $$x+y$$?

   • $$\frac{1}{3}$$
   • $$2$$
   • $$\frac{23}{9}$$
   • $$\frac{3}{5}$$

9. $$3(4x)+2(5y)=34$$$$-3(4x)+2(5y)=2$$What is the value of $$4x+5y$$?

   • 43/3

10. What system of linear equations is represented by the lines shown?From the graph, both lines intersect at: $$(8,0)$$First line (steeper):It appears to pass through $$(0,8)$$ and $$(8,0)$$Slope:$$m=\frac{0-8}{8-0}=-1$$Equation:$$y=-x+8$$Rewrite in standard form:$$x+y=8$$Multiply by $$4$$:$$4x+4y=32$$Second line (less steep):It appears to pass through $$(0,4)$$ and $$(8,0)$$Slope:$$m=\frac{0-4}{8-0}=-\frac{1}{2}$$Equation:$$y=-\frac{1}{2}x+4$$Rewrite in standard form:$$x+2y=8$$Multiply by $$4$$:$$4x+8y=32$$Now match with answer choices.Equivalent forms:First line:$$8x+4y=32$$Second line:$$-10x-4y=-64$$Final answer:

    • $$-8x-4y=32$$ and $$10x-4y=-64$$
    • $$8x+4y=32$$ and $$-10x-4y=-64$$
    • $$-8x-4y=32$$ and $$10x+4y=64$$
    • $$-8x+4y=32$$ and $$10x+4y=-64$$