Question

What are the solutions of the system? y=6x+6y=−x2+5x+6

Answer 1

x= -1 x= -1 and x= 6

Answer 2

Given the system of equations:

`y = 6x+6` .....[1]

`y = -x^2+5x+6` .....[2]

Equate these two equations we have;

`-x^2+5x+6 = 6x+6`

Subtract 6 from both sides we have;

`-x^2+5x= 6x`

Subtract 6x from both sides we have;

`-x^2-x= 0`

⇒
`-x(x+1) = 0`

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)