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# Find the solution set for the system of equations

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Find the solution set for the system of equations

{          6

{ ---------------- + 2x – y = 13

{      x+y

{

{         16

{ ---------------- + 2y – 4x = -12

{      x+y

Guest Sep 25, 2017
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#1
+1

2x^2 + xy - 13x + 6=y^2 + 13y..........(1)

2 x^2 + xy - 6 x =y^2 + 6y + 8..........(2)

Subtract (2) from (1) and we get:

x = 2 - y  and subbing this in (1) above we get:

y = -2      and subbing this in (2) above we get:

x = 4

Guest Sep 25, 2017
#2
+79654
+1

6

---------------- + 2x – y = 13       (1)

x + y

16                                                                                                      8

---------------- + 2y – 4x = -12        divide this through by 2     ⇒            ________  +  y - 2x   = -6        (2)

x + y                                                                                                    x + y

Rearrange   (2)   as            8       +    6               =   2x  - y

____

x + y

Sub this into (1)

6      +     8          +    6         =  13

___         ___

x + y       x + y

14        =        7

___

x + y

14   = 7 ( x  + y )

2  = x  + y      (3)

Sub (3) into (1)

6

__     + 2x  - y    =   13

2

3    +  2x  - y   =   13

2x  - y   = 10

y =  2x - 10     (4)

Sub  (4) into (3)

2  = x + 2x - 10

12 = 3x

4  = x

And   using (4)

y  = 2(4) - 10   = -2

CPhill  Sep 25, 2017

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