Question

Gina made tables of values to solve a system of equations. First, she found that the x-value of the solution was between 0 and 1, and then she found that it was between 0.5 and 1. Next, she made this table.
x y = 4x – 1 y = –3x + 5
0.5 1 3.5
0.6 1.4 3.2
0.7 1.8 2.9
0.8 2.2 2.6
0.9 2.6 2.3
1.0 3 2


Which ordered pair is the best approximation of the exact solution

A. (0.9, 2.4)
B. (0.7, 1.8)
C. (0.6, 2.5)
D. (0.9, 2.1)

Answer 1

Answer: Option A. (0.9,2.4)

Solution:

When x=0.8, we get in the first equation y=4x-1=2.2 and in the second equation y=-3x+5=2.6

When x=0.9, we get in the first equation y=4x-1=2.6 and in the second equation y=-3x+5=2.3

When we increase x from 0.8 to 0.9, in the first equation y increases from 2.2 to 2.6, and in the second equation y decreases from 2.6 to 2.3, then x must be between 0.8 and 0.9 and y must be between 2.3 and 2.6

Answer: Option A. (0.9,2.4)

Answer 2

We have that
y =  4x – 1 
y = –3x + 5

using a graph tool
see the attached figure

the exact solution is the point (0.857,2.429)
the answer is the option A. (0.9, 2.4)