Question

50 POINTS!!!!

Solve this system of equations

x = 3z − 5
2x + 2z = y + 16
7x − 5z = 3y + 19

Select the appropriate response:
A) 1, y = −2, z = 3
B) 5, y = −4, z = 1
C) 5, y = −8, z = 6
D) 4, y = −2, z = 3

Answer 1

D) x = 4, y = -2, z = 3

Explanation:

x = 3z − 5

2x + 2z = y + 16

2(3z - 5) + 2z = y + 16

6z - 10 + 2z = y + 16

8z = y + 26 ---> (A)

7x − 5z = 3y + 19

7(3z - 5) - 5z = 3y + 19

21z - 35 - 5z = 3y + 19

16z = 3y + 54 ---> (B)

8z = y + 26

16z = 3y + 54

2(y + 26) = 3y + 54

2y + 52 = 3y + 54

y = -2

8z = -2 + 26

8z = 24

z = 3

x = 3(3) - 5

x = 4

Answer 2

The answer is D

x = 4

y = -2

z = 3

Explanation:

Plug in the values of x and z into the first equation, and see that D is the only choice that is correct.