Question

Which ordered pair is the best approximation of the exact solution?

Answer 1

The correct option is A.

Explanation:

The given table represent the value of two functions

`y=-3x+6` .... (1)

`y=4x-5` .... (2)

Equate both the equations to find the solution of the equations.

`-3x+6=4x-5`

Isolate like terms.

`6+5=4x+3x`

`11=7x`

`(11)/(7)=x`

`x\approx 1.571`

Put this value in equation (1).

`y=-3(1.571)+6`

`y\approx 1.287`

The solution of the system of equation is

`(1.571, 1.287)\approx (1.6,1.3)`

Therefore approximation of the exact solution is (1.6,1.3). The correct option is A.

Answer 2

For this case what you should do is observe the table that the values of y of both functions are as similar as possible.
We observed that:
For the x 1.6 coordinate we have:

`y = 1.2 y = 1.4`
Therefore, a good approximation of the solution is:

`((1.2 + 1.4))/(2) = 1.3`
The ordered pair solution is:
(1.6, 1.3)
Answer:
(1.6, 1.3)option A