Simultaneous Equation

Question

Please may i get a step by step solution of how to solve

a^2 = 66 + ab

a = 3b + 4

 

I know the answer is a = 9 and b = 5/3

But i want to understand how to get there

Answer 1

a² =66+ab  ....eq 1      a= 3b+4.... eq 2

substituting the value of a from eq 2 to eq 1, we get,

(3b+4)² =66+(3b+4)b

9b² +24b+16 =66+3b² +4b

9b² +24b+16-66-3b² -4b=0

6b² +20b-50=0

3b² +10b-25=0

3b² +15b-5b-25=0

3b(b+5)-5(b+5)=0

(3b-5)(b+5)=0

3b-5=0                             or   b+5=o

b=5/3                               or   b=-5

a=3*5/3 +4 =9                  or a=3(-5)+4 =-15+4=-11