Question

Solve the system by the elimination method.
x + y - 6 = 0
x - y - 8 = 0
When you eliminate y , what is the resulting equation?

2x = -14
2x = 14
-2x = 14

Answer 1

Answer: The answer is b, 2x=14

Step-by-step explanation:

You add the equations...

2x-14=0

Move -14 over...

2x=14

Answer 2

Answer:  The correct option is

(B) 2x = 14.

Step-by-step explanation:  We are given to solve the following system of equations by the method of Elimination :

$x+y-6=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-y-8=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Also, to select the resulting equation when we eliminate y.

Adding equations (i) and (ii), we get

$(x+y-6)+(x-y-8)=0+0\\\\\Rightarrow 2x-14=0\\\\\Rightarrow 2x=14~~~~~~~~~~[\textup{this is the resulting equation}]\\\\\Rightarrow x=\dfrac{14}{2}\\\\\Rightarrow x=7.$

From equation (i), we get

$7+y-8=0\\\\\Rightarrow y-1=0\\\\\Rightarrow y=1.$

Thus, the required solution is (x, y) = (-1, 7) and the resulting equation while eliminating y is 2x = 14.

Option (B) is CORRECT.