Question

Which of the following equations could be the result of using the comparison method to solve the system shown?

x + y = 5
2x + y = 7
____________
a. -x - 5 = 7 - 2x
b. 5 - x = 7 - 2x
c. 5 - x = 2x - 7

Answer 1

The answer is b.
5 - x = 7 - 2x

Answer 2

Answer: The correct equation is (B)
`5-x=7-2x.`

Step-by-step explanation: We are given to select the correct equation that could be the result of using the comparison method to solve the following system :

`x+y=5~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x+y=7~~~~~~~~~~~~~~~~~~~~~~~(ii)`

Since the equation should be in the variable x, so we must compare the values of y.

From equations (i) and (ii), we have

`x+y=5~~~~~\Rightarrow y=5-x~~~~~~~~~~~~~~~~~(iii)\\\\2x+y=7~~~~\Rightarrow y=7-2x~~~~~~~~~~~~~~~~(iv)`

Comparing the values of y from equations (iii) and (iv), we get

`5-x=7-2x.`

Thus, the correct equation is
`5-x=7-2x.`

Option (B) is CORRECT.