what is th answer to this question x+y=11 x-y=7?

Question

the answer to this question

x+y=11

x-y=7

Answer 1

x + y = 11- - - - - Equation 1
x - y = 7- - - - - - Equation 2
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2x = 18

2x/2 = 18/2

x = 8/2

x = 9

The answer is x = 9

Insert the x value into equation 1

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x + y = 11

9 + y = 11

9 + y - 9 = 11 - 9

y = 2

The answer is y = 2

insert the y value into equation 1

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Check for equation 1

x + y = 11

9 + 2 = 11

11 = 11

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Check for equation 2

x - y = 7

9 - 2 = 7

7 = 7

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The solution set { 9, 7 }

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Answer 2

Sum the two equations

2x=18
x=9

9+y=11
y=2

Answer 3

add LHS and RHS

x+y+x-y=11+7

2x=18

=> x=9

x+y=11

9+y=11

y=11-9

y=2

Therefor x=9, y=2.

Answer 4

resolve for x and y A: x + ?y = 11 B: ?x + y = 7? => ?y = 11- x => (?y)^2 = (11- x)^2 => y = 121 -22x + x^2 sub into B: => ?x + y = 7 => ?x + 121 -22x + x^2 = 7 => ?x = - 114 +22x - x^2 => (?x)^2 = (- 114 +22x - x^2 )^2 resolve for x & examine solutions QED

Answer 5

x+y=11
+
x-y=7
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2x=18
x=9

9+y=11
y=2

solution set: (9,2)

* by the way i used the method of elimination