Question

Solve the system by the elimination method. -2x + y + 6 = 0 2x + y - 8 = 0 When you eliminate x, what is the resulting equation? 2y = 2 2y = -2 y = -2

Answer 1

I see you want to solve    -2x + y + 6 = 0 2x + y - 8 = 0    simultaneously.  Next time, please put each equation on its own line, like this:

-2x + y + 6 = 0

 2x + y - 8 = 0

or separate the two equations with "and" or some other symbol.

We can easily eliminate x by adding these 2 equations together:

-2x + y + 6 = 0 

 2x + y - 8 = 0

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       2y - 2 = 0, which yields y = 1.    This is the equation called for in this problem.                             You were not asked to find x.

Answer 2

Answer:  The solution is (x, y) = (3.5, 1).

The correct option is (A) $2y=2.$

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

$-2x+y+6=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x+y-8=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Also, to select the resulting equation while eliminating x.

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

$(-2x+y+6)+(2x+y-8)=0+0\\\\\Rightarrow 2y-2=0\\\\\Rightarrow 2y=2\\\\\Rightarrow y=\dfrac{2}{2}\\\\\Rightarrow y=1.$

Putting y = 1 in equation (i), we get

$-2x+1+6=0\\\\\Rightarrow -2x+7=0\\\\\Rightarrow 2x=7\\\\\Rightarrow x=\dfrac{7}{2}\\\\\Rightarrow x=3.5.$

Thus, the required solution is (x, y) = (3.5, 1) and the resulting equation equation  while eliminating x is $2y=2.$

Option (A) is CORRECT.