Question

Richard made tables of values to solve a system of equations. First he found

that the x-value of the solution was between 0 and 1, and then he found that it
was between 0.5 and 1. Next, he made this table.

Answer 1

(0.9,4.2)

Explanation:

Given:

The table above such that

`y = -x + 5`

`y = 6x - 1`

Required

Approximation of the solution

To do this, we start by equating both values of y

`-x + 5 = 6x - 1`

Collect like terms

`-x - 6x = -5 -1`

`-7x = -6`

Divide both sides by -7

`(-7x)/(-7) = (-6)/(=7)`

`x = (6)/(7)`

`x = 0.8571`

`x = 0.9` (Approximated)

Substitute
`(6)/(7)` for x in any of the expression of y

Using
`y = -x + 5`

`y = -(6)/(7)+ 5`

`y = (-6+35)/(7)`

`y = (29)/(7)`

`y = 4.1` (Approximated)

The closest to this is option D

(x,y) = (0.9,4.2)