- d.First, rewrite the system as the following
equivalent matrix equation as in Problem 917:
.
Next, identify the following determinants to be
used in the application of Cramer’s rule:
Since applying Cramer’s rule requires that we
divide by Din order to determine x and y,we
can conclude only that the system either has
zero or infinitely many solutions. We must
consider the equations directly and manipu-
late them to determine which is the case. To
this end, as in Problem 917, we note that the
second equation in the system is obtained by
multiplying both sides of the first equation by
–2. Therefore, the two lines are identical, so
the system has infinitely many solutions.
- d.First, rewrite the system as the following
equivalent matrix equation as in Problem 918:
.
Next, identify the following determinants to be
used in the application of Cramer’s rule:
Since applying Cramer’s rule requires that we
divide by Din order to determine x and y,we
can only conclude that either the system has
zero or infinitely many solutions. We must
consider the equations directly and manipu-
late them to determine which is the case. To
this end, as in Problem 918, note that multi-
plying both sides of the second equation by 3
yields the equivalent equation 6x+ 3y= 9.
Subtracting this from the first equation yields
the false statement 0 = –1. From this, we con-
clude that the two lines must be parallel
(which can also be checked by graphing
them). Hence, the system has no solution.
- a.First, rewrite the system as the following
equivalent matrix equation as in Problem 919:
.
Next, identify the following determinants to be
used in the application of Cramer’s rule:
So, from Cramer’s rule, we have:
Thus, the solution is x= – 171 ,y= – 252 .
y== =DDy – 225 – 225
x== =DDx –^1422 – 117
D ()()()()
3
4
1
3 33 41 5
–
y==– ––– =
Dx==–^1342 ()() ( )() 12 ––34 14=
D==– 43 42 ( )() ()()–– 32 44 =– 22
x
y
3
4
4
2
1
3
–
>>>HH H= –
D^6 ()() ()()
2
8
3
y==^63 – 28 2=
Dx==^8331 ()() ()() 81 –– 33 = 1
D==^6213 ()() ()() 61 – 23 0=
x
y
6
2
3
1
8
>>>HH H= 3
D ()()()()
1
2
3
6 16 23 0
–
y==– ––– =
Dx==––^3624 ()()()() 34 –––62 24=–
D==– 21 –^24 ()()()()–––14 22 0=
x
y
1
2
2
4
3
6
–
>>>––HH H=
ANSWERS & EXPLANATIONS–
