Answer:
#7: (p, r) = (0, -2) #8: (z,w) = z, +
z), ∈R #9: (c,d) = (3,3) #10: (u,x) ∈∅ #11: (a,b) = (-1, 2) #12:
Step-by-step explanation:
#7
Solve for 2p
2p - 3r = 6
2p = -6 -3r
substitute the given value of 2p into equation 2p - 3r = 6
-6 - 3r - 3r = 6
solve for r
r= -2
substitute value of r in equation
2p = -6 - 3x (-2)
solve for p
p=0
solution is ordered pair (p,r) = (0, -2)
#8
Solve for w
w= +
z
substitute the given value of w into equation
6 ( +
z) - 8z = 16
solve for z
z ∈ R
The statement is true for any value of z and w that satisfy both equations from the system. Therefore, the solution is in parametric form.
(z,w) = z, +
z)
#9
Solve for c
c + d = 6
c = d
substitute the given value of c into equation c + d = 6
d + d = 6
solve for d
d=3
substitute value of d in equation
c=3
solution is ordered pair (c,d) = (3,3)
#10
Solve for u
u= 3-2x
substitute the given value of c into equation
2 (3-2x) +4x = -6
solve for x
x ∈∅
Since the system has no solution for x the answer is
(u,x) ∈∅
#11
Solve for b
b= 5+3a
substitute the value of b into equation
3a + 5 + 3a+ b = -1
solve for a
a= -1
substitute the value of a into equation
b= 5 + 3x (-1)
solve for b
b=2
solution is ordered pair (a, b) = (-1, 2)