(a) (i)
y
= 100 – 2
x,
(ii)
y
= 10 +
x
(b) (i)
y
= 100 –
x,
(ii)
y
= 10 + 0.5
x
(c)
(i)
y
= 100 –
x,
(ii)
y
= 10 + 2
x
(d) (i)
y
= 100 + 2
x,
(ii)
y
= 10 +
x
3.
Solve the following pairs of equations, and compare your results for (a) with (b), (c),
and (d):
(a) (i)
y
= 20 +
x,
(ii)
y
= 10 + 2
x
(b) (i)
y
= 20 + 0.5
x,
(ii)
y
= 10 +
x
(c)
(i)
y
= 20 + (1/3)
x,
(ii)
y
= 10 + (2/3)
x
(d) (i)
y
= 30 +
x,
(ii)
y
= 10 + 2
x
4.
Find the general solution for
x
and
y
, given the following equations:
(i)
y
=
a
1
+
b
1
x,
(ii)
y
=
a
2
+
b
2
x
.
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MATH MODULE 3: SOLVING LINEAR EQUATION SYSTEMS
M33
5.
The following pairs of equations refer to 3 different markets. In each market, Price (
P
,
measured in dollars per unit) is on the vertical axis and Quantity (
Q
, measured in
units) is on the horizontal axis. In each case, give the equilibrium values for
P
and
Q.
(a)
(i) Demand:
P
= 40 – 0.005
Q
D
;
(ii) Supply:
P
= 12 + 0.002
Q
S
(b)
(i) Demand:
P
= 40 – 0.05
Q
D
,
(ii) Supply:
P
= 20
(c)
(i) Demand:
Q
D
= 40 – 2
P,
(ii) Supply:
Q
S
= –30 +
P
6
.
The supply curve for the Ergonomic Bagel (EB) industry is given by the equation
P
S
= 20 + 0.1
Q
S
, where
P
S
is in $/case and
Q
S
is in cases.
(a)
The government is trying to decide on the best sales tax to impose on EBs: a unit
tax (
T
) of $25/case, which would make the taxridden supply curve facing buy
ers equal to
P
S
+
T, or
an
ad valorem
(or percentageofvaluebased) tax at rate
t
=
25%, which would make the taxridden supply curve facing buyers equal to
P
S
(1+
t
). At what level of
Q
S
is the level of the tax the same under both systems,
and what is the price facing buyers at this point?
(b)
If the supply curve is as it was initially, the
ad valorem
tax rate is 25%, and the
ad
valorem
and unit taxes would be equal when
Q
S
= 150 cases, then how much is
the unit tax?
7. Both “SweetTooth” Sal and Sourdough Slim have the same budget per period,
which they both spend entirely on containers of Jam (on the vertical,
y
, axis) and
loaves of Bread (on the horizontal,
x
, axis): the equation for the budget line of each is
y
= 120 – (2/3)
x.
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 Fall '12
 Danvo
 Equations, Elementary algebra, linear equation systems, Equation Systems

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