Can you help me find the x, y for these equations?

Question

x + 3y = 14
x - y = -14

-x - 2y = 9
3x - 5y = -16

Answer 1

x + 3y = 14- - - - - - Equation 1
x - y = - 14- - - - - - -Equation 2
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Substitute Method equation 2

x - y = - 14

x - y + y = y - 14

x = y - 14

Substitute the x value into equation 1

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x + 3y = 14

y - 14 + 3y = 14

4y - 14 = 14

4y - 14 + 14 = 14 + 14

4y = 28

4y / 4 = 28 / 4

y = 28 / 4

y = 7

Insert the y value into equation 1

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x + 3y = 14

x + 3(7) = 14

x + 21 = 14

x + 21 - 21 = 14 - 21

x = - 7

Insert the x value into equation 1

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Check for equation 1

x + 3y = 14

- 7 + 3(7) = 14

- 7 + 21 = 14

14 = 14

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Check for equation 2

x - y = - 14

- 7 - 7 = - 14

- 14 = - 14

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Both equations balance

The solution set is { - 7, 7 }

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Answer 2

x+3y =14 -------------------------------(1)
x-y= -14 --------------------------------(2)
(1) -(2)
x+3y =14
-x+y=14
________
0+4y =28
y=28/4 =7
x +3y =14
x+3(7) =14
x=14-21 .
x= -7

-x -2y=9 --------------(1)
3x-5y = -16 ------------(2)
(1) -x =9+2y x= -9 -2y
(2) 3( -9 -2y) -5y =-16
-27 -6y -5y =-16
-27 -11y =-16
-11y =-16 +27
-11y =11
y = - 1
x=-9 -2y
=-9 -2(-1)
= -9 +2
x=7

Answer 3

(i) x + 3y = 14
(ii) x - y = -14 -------------> (iia) x = y - 14
(iia) and (i) ------------------> (y-14) + 3y = 14
simplify 4y - 14 = 14
or 4y = 28
so y = 7
back to (i) x + 3(7) = 14
simplify x + 21 = 14
so x = 14 - 21 or x = -7

check via (ii) . . . (-7) - (7) = -14 . . . is true!

Answer 4

x=14-3y
(14-3y)-y=-14
-4y=-28
y=7
x=14-3(7)
x=14-21
x=-7

-x=2y+9
x=-2y-9
3(-2y-9)-5y=-16
-6y-27-5y=-16
-11y=11
y=-1
x=-2(-1)-9
x=-7