Question

D
7. Solve the system:
f(x)=(x-3)² +1
g(x)=-3x+10

Answer 1

Answer: (0,10) and (3,1)

Explanation:

Before I solve the system, I am going to rewrite it to make it easier for me to understand it.

`y=(x-3)^2+1\\y=-3x+10`

Notice that f(x) and g(x) have been changed into y. The reason is because f(x) and g(x) are the same and stand for y, but we only use f and g to distinguish between the 2 equations. We can use equal values to solve.

`(x-3)^2+1=-3x+10` [exponent]

`x^2-6x+9+1=-3x+10` [add both sides by 3x]

`x^2-3x+10=10` [subtract both sides by 10]

`x^2-3x=0` [factor]

`x(x-3)=0`

Notice that x=0 and x-3=0. This means the solutions are x=0 and x=3.

To find the actual full solution, we have to plug those points back into the original equations.

`-3(0)+10=0+10=10\\-3(3)+10=-9+10=1`

Therefore, the solutions to this system are (0,10) and (3,1).