Question

‼️‼️solve by substitution {2p-3r=6

Answer 1

Answer:

#7: (p, r) = (0, -2) #8: (z,w) = z, $\frac{8}{3}$ + $\frac{4}{3}$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= $\frac{8}{3}$ + $\frac{4}{3}$z

substitute the given value of w into equation

6 ($\frac{8}{3}$ + $\frac{4}{3}$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, $\frac{8}{3}$ + $\frac{4}{3}$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)