Question

Nevin made tables of values to approximate the solution to a system of equations. First he found that the x-value of the solution was between 1 and 2, and then he found that it was between 1 and 1.5. Next, he made this table. y= 4x-3 = -5x+9 1 1 3.5 3 2.5 2 2 1.5 1.5 Which ordered pair is the best approximation of the exact solution?

Answer 1

It would be B. (1.3,2.3).

Answer 2

Given the following System of equations:

`\mleft\{\begin{aligned}y=4x-3 \\ y=-5x+9\end{aligned}\mright.`

You can find the exact solution as following:

1. You can make both equation equal to each other:

`4x-3=-5x+9`

2. Now you must solve for the variable "x" in order to find its value. This is:

`\begin{gathered} 4x+5x=9+3 \\ 9x=12 \\ x=(12)/(9) \\ \\ x=(4)/(3) \\ x=1.33 \end{gathered}`

3. Substitute the value of "x" into any original equation and evaluate, in order to find the value of "y":

`\begin{gathered} y=4x-3 \\ y=4(1.33)-3 \\ y=2.32 \end{gathered}`

Then you get this solution written as an ordered pair:

`(1.33,2.32)`

You can determine that the best approximation of the exact solution is: Option A.