Question

Approximate the solution to the system of equations.

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

a. How do you know what the solution is between the two rows in the table corresponding to x=0.5 and x=1
Table:
x y=-x+3 y=2x+1
-1 4 -1
-0.5 3.5 0
0 3 1
0.5 2.5 2
1 2 3
1.5 1.5 4
2 1 5

b Complete the table to show the values of x between 0.5 and 1. I already did this

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

c. Which tow x values will the solution be between?>

d. Identify a reasonable approximation for the solution of this system

Answer 1

An easier way to understand d. since a., b., and c. have already been answered, is like this: You're looking for a reasonable approximation right?

So it doesn't matter where it is between the points x=0.6 and x=0.7.

The funny thing is that 0.6 = 0.60 and 0.7 = 0.70 so .61 .62 .63 .64 .65 .66 .67 .68 .69 .70, right?

Just relax and cut it in half! 0.65 is a reasonable approximation for the solution of x!

This is the same as dividing the sum (0.6 + 0.7) /2 by two getting it's half!

Do the same for the y-values. So since there are two different lines it could be, according to the graph. y= 2.4 0r y= 2.3 the ones that show greater similarity. The other answer explains the similarity part better. Just do the same and divide the sum of both decimals by 2.

The other answer shows the decimal you would get! But try it out first even if your not in a jolly mood.

Hope this helped!

Answer 2

a) at x=0.5 y=2 and at x=1 y=2 this similarity in values shows that the solution for x is between 0.5 and 1

c) The x solution will be between x=0.0 and x=0.7 .

There is a similarity in values of y at x=0.6, y=2.4 and at x=0.7 , y=2.4

d) For x= (0.6+0.7)/2 = 1.3/2 =0.65

For y= (2.4+2.3)/2 =4.7/2=2.35

Approximate solution is (0.65, 2.35)