Question

Identify the system of equations that is not satisfied by the given ordered pair.

(3, −2) or p = 3, q = − 2

A. 23p = 7 − 31q
31p + 23q = 47

B. 5q = −3p − 1
p = 2 + 3q

C. 5q = −3p − 1
−2p + 3q = −12

D. p + 3q = −3
2q = 5 − 3p

Answer 1

Option B

The ordered pair (3, -2) is not a solution to 5q = −3p − 1 and p = 2 + 3q

Solution:

Given ordered pair is (3, -2)

p = 3 and q = -2

We have to find the system of equations that is not satisfied by the given ordered pair

Option A

23p = 7 − 31q

31p + 23q = 47

Substitute p = 3 and q = -2 in both equations

23(3) = 7 - 31(-2)

69 = 7 + 62

69 = 69

Thus satisfied

Check the next equation

31p + 23q = 47

31(3) + 23(-2) = 47

93 - 46 = 47

47 = 47

Thus this equation is also satisfied

The given ordered pair is a solution to system of equations

Option B

5q = −3p − 1

Substitute p = 3 and q = -2

5(-2) = -3(3) - 1

-10 = -10

Thus satisfied

Check the next equation

p = 2 + 3q

3 = 2 + 2(-2)

3 = 2 - 4

`3 \\eq -2`

Thus ordered pair is not satisfied

The given ordered pair is not a solution to system of equations

Option C

5q = −3p − 1

Substitute p = 3 and q = -2

5(-2) = -3(3) - 1

-10 = -9 - 1

-10 = -10

Thus satisfied

Check the next equation

−2p + 3q = −12

-2(3) + 3(-2) = -12

-6 - 6 = -12

-12 = -12

Thus satisfied. The given ordered pair is a solution to system of equations

Option D

p + 3q = −3

Substitute p = 3 and q = -2

3 + 3(-2) = -3

3 - 6 = -3

-3 = -3

Thus satisfied

Check next equation

2q = 5 - 3p

2(-2) = 5 - 3(3)

-4 = 5 - 9

-4 = -4

Thus satisfied. The given ordered pair is a solution to system of equations