Use mathematical induction to show that (a) 1 + 4 +7 + +(3n -2) = n (3n - 1)/2 for n is the element of natural numbers, n is greater than or equal to 1.(

It is true for  n=1if n=k is true then n=k+1 is also true

Step-by-step explanation:

n=1:

      TRUE

n=k:

n=k+1:

We replace the first part of the equation with our value for n=k:

we develop both sides of the equation to verify equality:

      TRUE

x = 0
y = -3

Explanation:
The first given equation is:
x = 3 + y > I
The second given equation is:
21x + 8y = -24 > II

Substitute with I in II and solve for y as follows:
21x + 8y = -24
21(3+y) + 8y = -24
63 + 21y + 8y = -24
29y = -24 - 63
29y = -87
y = -3

Substitute with y in equation I to get x as follows:
x = 3 + y
x = 3 + (-3)
x = 3 - 3
x = 0

Hope this helps :)