Answer:
1) We have the system:
5*x - 3*y = 15
4*x + 3*y = 6
To solve this, we first need to isolate one of the variables in one of the equations, let's isolate x in the first equation:
x = 15/5 + (3/5)*y = 3 + (3/5)*y
Now we can replace this in the other equation to get:
4*( 3 + (3/5)*y) + 3*y = 6
and solve this for y.
12 + (12/5)*y + 3*y = 6
(12/5 + 3)*y = 6 - 12 = -6
(12/5 + 15/5)*y = -6
(27/5)*y = -6
y = -6*(5/27) = 1.11
Now we can replace this in the equation:
x = 3 + (3/5)*y
To get the value of x.
x = 3 + (3/5)*1.11 = 3.67
Then the solution of this system is the point (3.67, 1.11)
2) Now we have the system:
2*x + 5*y = 26
4*x + 3*y = 24
The solution method is the same as before:
x = 26/2 - (5/2)*y = 13 - (5/2)*y
Now we replace this in the other equation:
4*( 13 - (5/2)*y) + 3*y = 24
52 - 10*y + 3*y = 24
52 - 7*y = 24
52 - 24 = 7*y
28 = 7*y
28/7 = y
4 = y
now we replace this in the equatio:
x = 13 - (5/2)*y
x = 13 - (5/2)*4 = 13 - 10 = 3
The solution of this sytem is (3, 4)
3) Now we have the system:
3*x + 3*y = 39
2*x - 3*y = -2
first we isolate x in the first equation:
x = 39/3 - 3*y/3 = 13 - y
Now we can replace this in the other equation:
2*(13 - y) - 3*y = -2
26 - 2*y - 3*y = -2
26 - 5*y = -2
26 + 2 = 5*y
28 = 5*y
28/5 = y = 5.6
Now we can replace this in the equation:
x = 13 - y
To get the x-value
x = 13 - 5.6 = 7.4
Then the solution for this system is (7.4, 5.6)
such that
, and because the distribution is symmetric about its mean, it follows that 
.
.