Find x and y is 2x+ y= 11 and x^2 - y^2 = 24

2x+ y = 11.............(1)

x^2 -
y^2 = 24............(2)

First we will rewrite
(1):

2x + y = 11

==> y= 11-
2x

Now we will substitute in
(2):

==> x^2 - y^2 =
24

==> x^2 - ( 11-2x)^2 =
24

==> x^2 - ( 121 - 44x + 4x^2 ) =
24

==? x^2 - 121 + 44x - 4x^2 =
24

==> -3x^2 + 44x - 121 - 24 =
0

==> -3x^2 + 44x - 145 = 0

Now
we will calculate the roots:

==> x1= ( -44 + sqrt( 44^2
-4*-3*-145) / 2*-3

               = ( -44 + 14) / -6 = -30/-6 =
5

==> x1= 5  ==> y1= 11-2*5= 1==>
y1= 1

==> x2= ( -44 - 14) /-6 = -58/ -6 =
29/3

==> x2= 29/3  ==> y1= 11-2*29/3 =
-25/3