Question

Which of the following would not be the result of a substitution in the following system? 2x + y = 7 y - x = 1
A) 7 - 2x - x = 1
B) 2x + x + 1 = 7
C) 2(y + 1) + y = 7

Answer 1

Answer: Option C.

Step-by-step explanation:

A) The result of the substitution shown in Option A is obtained by solving for y from the first equation and substituting into the second equation:

$2x + y = 7\\y=7-2x$

$y - x = 1\\7-2x-x=1$

Therefore, this is a result of a substitution in the given system.

B) The result of the substitution shown in Option B is obtained by solving for y from the second equation and substituting into the first equation:

$y - x = 1$

$y=x+1$

$2x + y = 7\\2x + x + 1 = 7$

Therefore, this is a result of a substitution in the given system.

C) The result of the substitution shown in Option C is not  a result of a substitution in the given system, because if you solve for x from the second equation and substitute into the first one, you get:

$y-x=1\\(-1)(-x)=(-y+1)(-1)\\x=y-1\\\\2(y - 1) + y = 7$