Question

Someone please help me I’m having trouble!!!!

Answer 1

(c)
`x = 0.6` and
`x = 0.7`

(d)
`(x,y) = (0.67,2.33)`

Explanation:

Given

See attachment

First, we complete the table

`y = -x + 3`
`y = 2x + 1`

`y = -0.6 + 3 = 2.4`
`y = 2 * 0.6 + 1 = 2.2`

`y = -0.7 + 3 = 2.3`
`y = 2 * 0.7 + 1 = 2.4`

`y = -0.8 + 3 = 2.2`
`y = 2 * 0.8 + 1 = 2.6`

`y = -0.9 + 3 = 2.1`
`y = 2 * 0.9 + 1 = 2.8`

So, we have:

`\begin{array}{ccc}x & {y = -x + 3} & {y = 2x + 1} & {0.5} & {2.5} & {2} & {0.6} & {2.4} & {2.2} & {0.7}&{2.3} & {2.4} & {0.8}&{2.2} & {2.6} & {0.9}&{2.1} & {2.8} & {1}&{2} & {3} \ \end{array}`

Solving (c): Between which values is y

The values of y are for both equations are closest at:

`x = 0.6` and
`x = 0.7`

Hence, the solution is between

`x = 0.6` and
`x = 0.7`

Solving (d): Approximated value of the solution

We have:

`y = -x + 3`

`y = 2x + 1`

`y=y`

So:

`-x + 3 = 2x + 1`

Collect like terms

`2x + x = 3 - 1`

`3x= 2`

Divide both sides by 3

`x = 0.67`

Substitute
`x = 0.67` in
`y = -x + 3`

`y =-0.67 + 3`

`y =2.33`

So, the solution is:

`(x,y) = (0.67,2.33)`