Answer:
Given the system of equations:
[tex]y = 6x+6[/tex] .....[1]
[tex]y = -x^2+5x+6[/tex] .....[2]
Equate these two equations we have;
[tex]-x^2+5x+6 = 6x+6[/tex]
Subtract 6 from both sides we have;
[tex]-x^2+5x= 6x[/tex]
Subtract 6x from both sides we have;
[tex]-x^2-x= 0[/tex]
⇒[tex]-x(x+1) = 0[/tex]
By zero product property we have;
⇒x = 0 and x+1= 0
⇒x = 0 and x=-1
Substitute these values in [1] we have;
For x = 0
y = 6(0)+6 = 6
for x = -1
y =6(-1)+6 = -6+6= 0
Therefore, the solutions of the given systems are, (0, 6) and (-1, 0)
