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:
For this case we have the following system of equations: [tex]y = 6x - 30
y = x ^ 2 - 18x + 114[/tex] Equaling both equations we have: [tex]x ^ 2 - 18x + 114 = 6x - 30
[/tex] From here, we rewrite the polynomial: [tex]x ^ 2 - 18x + 114 - 6x + 30 = 0
[/tex] Adding similar terms we have: [tex]x ^ 2 - 24x + 144 = 0
[/tex] Factoring we have: [tex](x-12) (x-12) = 0
[/tex] Therefore, the solution is: [tex]x = 12[/tex] (multiplicity 2) Substituting the value of x in any of the equations we find the value of y: [tex]y = 6 (12) - 30
y = 72 - 30
y = 42[/tex] Therefore, the ordered pair solution is: [tex](a, b) = (12, 42)
[/tex] Answer: the value of b is: [tex]b = 42[/tex]
