Question

PLEASE HELP VERY URGENT!!!!!!!

Lucy made tables of values to approximate the solution to a system of
equations. First she found that the x-value of the solution was between 1 and
2, and then she found that it was between 1.5 and 2. Next, she made this
table.

Which ordered pair is the best approximation of the exact solution?
O A. (1.7,0.9)
B. (1.5, 1.8)
C. (1.6, 1.3)
D. (1.9.1.5)

Answer 1

The correct option is;

C. (1.6, 1.3)

Explanation:

Given that at x = 1.5 the y-values of both equations are y = 1.5 and y = 1 respectively

The x-value > The y-value

The difference in the y-values = 1.5 - 1 = 0.5

At x = 1.6 the y-values of both equations are y = 1.2 and y = 1.4 respectively

The x-value > The y-value

The difference in the y-values = 1.2 - 1.4 = -0.2

At x = 1.7 the y-values of both equations are y = 0.9 and y = 1.8 respectively

The x-value > The first y-value and the x-value < the second y-value

The difference in the y-values = 0.9 - 1.8 = 0.9

Therefore, the approximate y-value can be found by taking the average of both y-values when x = 1.6 where the difference in the y-values is least as follows;

Average y-value at x = 1.6 = (1.2 + 1.4)/2 = 1.3

Therefore, the best approximation of the exact solution is (1.6, 1.3)

By calculation, we have;

-3·x + 6 = 4·x - 5

∴ 7·x = 11

x = 11/7 ≈ 1.57

y = 4 × 11/7 - 5 ≈ 1.29

The solution is (1.57, 1.29)