Answer:

** [B]:** “

**contains one point**” .

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Explanation:

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Given:

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x + y = 6 ;

x – y = 0 ;

**_________________** To solve for “x” ;

Consider the first equation:

x + y = 6 ;

subtract “y” from each side of the equation ; to isolate “x” on one side of the equation; and to solve for “x” ;

x + y – y = 6 – y ;

x = 6 – y ;

**________________**

Take the second equation:

**____________________**

x – y = 0 ;

Solve for “x” ;

Add “y” to EACH SIDE of the equation; to isolate “x” on one side of the equation; and to solve for “x” ;

x – y + y = 0 + y ;

**________________________________**

x = y

**______________**

x = 6 – y

Substitute “x” for “y” ;

x = 6 – x ;

Add “x” to Each side of the equation:

**_______________________________**

x + x = 6 – x + x ;

2x = 6 ;

Now, divide EACH SIDE of the equation by “2” ; to isolate “x” on one side of the equation; and to solve for “x” ;

2x/2 = 6/2 ;

x = 3 .

**_______________**

Now, since “x = 3” ; substitute “3” for “x” in both original equations; to see if we get the same value for “y” ;

**_______________________________**

x + y = 6 ;

x – y = 0

**________________________________**

Start with the first equation:

**________________________________**

x + y = 6 ;

3 + y = 6 ;

Subtract “3” from each side of the equation; to isolate “y” on one side of the equation; and to solve for “y” ;

3 + y – 3 = 6 – 3 ;

y = 3 .

**________________________**

Now, continue with the second equation; {Substitute “3” for “x” to see the value we get for “y”} ;

**________________________**

The second equation given is:

**________________________**

x – y = 0 ;

Substitute “3” for “x” to solve for “y” ;

3 – y = 0 ;

Subtract “3” from EACH side of the equation:

3 – y – 3 = 0 – 3 ;

-1y = -3 ;

Divide EACH side of the equation by “-1” ; to isolate “y” on one side of the equation; and to solve for “y” ;

-1y/-1 = -3/-1 ;

y = 3 .

**________________________**

So, for both equations, we have one value: x = 3, y = 3; or: write as:

“(3, 3)” ; { **which is:** “**one single point**” ; which is: **Answer choice: [B]** } .

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