Answer: [B]: "contains one point" . _______________________________ Explanation: __________________ Given: __________________ 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] } . __________________________________________________________