Question

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

Answer 1

Answer:

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

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

Step-by-step 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:

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