1.	Give the solution to y in the system:  y = 9 ? 2x and 2x ? 5y = 15.
A)	y=1
B)	y=5
C)	 

D)	y=?1


2.	Give the solution to x in the system:  3x + 2y = 3 and 63x ? 36y = 11.
A)	x=2
B)	 

C)	 

D)	 



3.	Sesame Street on Stage has different ticket prices for adults and
for children under 6.  Beth and her two children, ages 3 and 4, paid
$15 to gain entrance, while Jamie and John Jacobs and their 2-year-old
daughter got in for $19.50.  What is the ticket price for adults?
A)	$3.50
B)	$5.75
C)	$8.00
D)	$9.00


4.	Solve the system for y.
2x + y = 3
2x + y = ?1
A)	Inconsistent
B)	y= 2
C)	y= ?3
D)	y=4


5.	Solve the system for x.
2x + 3y = 1
5x + 3y = 16
A)	x=2
B)	x=0
C)	x=5
D)	x=?3


6.	Solve the system for y.
?7x + y = 12
5x ? 9y = 8
A)	y= 2
B)	y=?2
C)	y=4
D)	Dependent


7.	Solve the system for x
x + y = 2
x = 4y + 5
A)	x=13/5
B)	x=?3/5
C)	x=?13/5
D)	x=3/5


8.	Solve the system for y.
x + y = ?3
x ? 2y = ?5
A)	y= 2/3
B)	y=?11/4
C)	y= ?3
D)	y=1/5


9.	Solve the system for y.
?3x ? y = ?4
?3x ? 7y = ?3
A)	y=?25/18
B)	y= ?4/6
C)	y=?1/12
D)	y=?1/6


10.	Solve the system for x.
?4x + 2y = ?5
2x ? 4y = 3
A)	x=7/6
B)	x=?1/2
C)	x=4/6
D)	x=7


11.	The definition of an inconsistent system could be
A)	A system where two equations are the same line
B)	A system of independent equations
C)	A system of parallel lines
D)	A system of two inequalities


12.	The system 4x ? 24y = 32 and x ? 6y = 8 has no solution.
A)	True
B)	False


13.	Find the point of intersection of the horizontal line through the
point (3, ?2) and the line whose equation is 2x ? 3y = 6.
A)	(3, 0)
B)	(3, ?4)
C)	(3, ?2)
D)	(0, ?2)


14.	If two lines intersect in a single point, a system consisting of
these two linear equations is:
A)	dependent
B)	inconsistent
C)	independent
D)	systematic

Hi cleanncrazi!

I will post the answers right now, to get them to you as fast as
possible, and I will immediately follow that up with a clarification
with the step by step method of finding those answers.

1.  D)  y = -1
2.  x = 5/9
3.  C)  $800
4.  A)  Inconsistent
5.  C)  x = 5
6.  B)  y = -2
7.  A)  x= 13/5
8.  A)  y= 2/3
9.  D)  y= ?1/6
10. A)  x=7/6
11. C)	A system of parallel lines
12. B)  False
13. D)  (0, ?2)
14. C)  Independent

Cheers,
tox-ga

---

Clarification of Answer by tox-ga on 16 Jun 2004 00:01 PDT

Hi!

Sorry, there is a slight typo in my answer to question 3.  I forgot
the decimal point; the answer is C) $8.00, not eight hundred dollars.

Here are some step-by-step solutions.

1.  First, isolate x in each equation:
y = 9 ? 2x => 2x = 9 - y
2x ? 5y = 15 => 2x = 15 + 5y
Now 2x = 2x, so we can eliminate that variable:
9 - y = 15 + 5y      and now solve for y
6y = -6
 -> y = -1

2.  We use essentially the same method: isolate a variable and eliminate it
3x + 2y = 3 => y = -1.5x + 1.5
63x ? 36y = 11 => y = 63/36x - 11/36 (after dividing by -36 and moving the x)

63/36x - 11/36 = -1.5x + 1.5
117/36x = 65/36
x = 65/117 = 5/9

3. 
let a = the price an adult pays
let c = the price a child pays
Beth and her two children, ages 3 and 4, paid $15...
 this means that an adult ticket and 2 child tickets cost 15
 so: a + 2c = 15
Jamie and John Jacobs and their 2-year-old daughter got in for $19.50
 so: 2a + c = 19.5
Solving these two equations using the same method as above (isolate
and eliminate c)
we get a = 8
So the adult pays $8.

4.  Solving for y means we should isolate and eliminate x
2x + y = 3 => 2x = -y + 3
2x + y = ?1 => 2x = -y - 1
-y + 3 = -y - 1      add y to both sides and we get
3 = -1
  this is clearly impossible, so that means no pair of numbers x and y
  could satisfy the system of equations.  This means it is inconsistent.

5.
2x + 3y = 1 => 3y = -2x + 1
5x + 3y = 16 => 3y = -5x + 16
2x - 1 = 5x - 16
3x = 15
-> x = 5

6 to 10 is essentially more of the same, isolating and eliminating
variables.  If you would like some help with the steps to these, just
ask and I'll be glad to provide it.


11.  An inconsistent system is one with no solutions.  In terms of two
lines, it would be two lines which do not cross ever.  This means the
lines are parallel.


12.  Notice that 4x ? 24y = 32 is just four times x ? 6y = 8 so
really, these describe the same line.  That means this system has
infinitely many solutions, not no solutions.  False.


13.
The horizontal line running through (3, -2) is y = -2.  Solving y = -2
and 2x ? 3y = 6
we get 2x ? 3(-2) = 6 => 3x + 6 = 6 => x = 0
so the point is (0,-2)


14.  If two lines intersect at a single point, 
 - they are not dependent, since dependent lines intersect at
infinitely many points
 - they are not inconsistent, since inconsistent lines do not intersect
 - to be honest, I have no idea what 'systematic' could mean
but they definitely are independent, as independent lines intersect at one point.

Cheers,
tox-ga

This was wonderful!!!!!!!!

Ahah, the Joy of Internet.... If you don't have a big brother or a big
sister to do the homework for you, you have google now.

I agree with you, Jazar :)

If I was a teacher I would be looking at these boards and usenet for
this type of thing.  Then in class I would point out that I had found
someone doing this.  It doesn't promote learning.

I guess for 40 doller's the google researcher looked past the TOS.

Scubajim:

And if were an English teacher, I'd point out that your sentence
should read, "If I were a teacher..."