Question

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

Answer 1

Answer:
`5-x=7-2x`

Explanation:

Given equations:
`x+y=5\\\Rightarrow\ y=5-x..........(1)\\2x+y=7\\\Rightarrow\ y=7-2x.........................(2)`

Comparing equation (1) from equation (2), we get

`5-x=7-2x`

• Comparison method is a method for solving systems of independent equations by starting rewriting both equations with the same variable and then compare.

Hence,
`5-x=7-2x` is the result of using the comparison method to solve the system shown.

Answer 2

Option (2) is correct.

Explanation:

Given : two a system of linear equation as

x+ y = 5 and

2x+ y = 7

We have to choose out of given options that could be the result of using comparison method to solve the given system .

COMPARISON METHOD

In comparison method we find a value for the single variable in term of others in given equations and compare the two equations.

Here, we first find the value of y in both equation and then compare,

Thus, x+ y = 5 ...........(1)

2x+ y = 7 .........(2)

From (1) , y = 5- x ..........(3)

And from (2) , y = 7- 2x ......(4)

Now, comparing (3) and (4) , we have,

5- x = 7- 2x

Thus, option (2) is correct.