Question

If you were to use the substitution method to solve the following system, choose the new system of equations that would result if x was isolated in the second equation.

5x – 2y – z = 16
x + y + 4z = 6
3x + 2y + 6z = 16

Choices:



A)–7y – 21z = –14
–y – 6z = –2

B)7x + 7z = 28
x – 2z = 4

C)–3y + 19z = –14
5y + 18z = –2

D)21x – 7y = 70
33x – 10y = 112

Answer 1

c

Answer 2

How do you work it out?

Answer 3

Lets first clear the variable x in the second equation which we will have:\[x+y+4z = 6\] turns into \[x = 6-y -4z\]. Now that we have cleared for x, substitute (that's where the name comes from) that variable for all the other x's that you have in both equations: First equation you will have:\[5(6-y-4z) -2y -z = 16\] which turns into \[30 - 5y - 20z -2y -z =16\] which implies\[-7y -21z = -14\]. Now using this same algorithm you have that \[3(6-y-4z)+2y+6z =16\] which implies that\[18-3y-12z +2y+6z=16\] which finishes into \[-y-6z=-2\]. Therefore the answer is A. Peace, Love and Happiness from Puerto Rico.

Answer 4

Thank u so much! :)