Question

Y y ​ =6x−30 =x 2 −18x+114 ​ if (a,b)(a,b)left parenthesis, a, comma, b, right parenthesis is the solution to the system of equations shown above, what is the value of bbb? answer:

Answer 1

For this case we have the following system of equations:

`y = 6x - 30 y = x ^ 2 - 18x + 114`
Equaling both equations we have:

`x ^ 2 - 18x + 114 = 6x - 30`
From here, we rewrite the polynomial:

`x ^ 2 - 18x + 114 - 6x + 30 = 0`
Adding similar terms we have:

`x ^ 2 - 24x + 144 = 0`
Factoring we have:

`(x-12) (x-12) = 0`
Therefore, the solution is:

`x = 12` (multiplicity 2)
Substituting the value of x in any of the equations we find the value of y:

`y = 6 (12) - 30 y = 72 - 30 y = 42`
Therefore, the ordered pair solution is:

`(a, b) = (12, 42)`
Answer:
the value of b is:

`b = 42`