Question

Philip made tables of values to solve a system of equations. First, he found that the x-value of the solution was between 0 and 1, and then he found that it was between 0.5 and 1. Next, he made this table.


x y = –2x + 3 y = 5x – 1

0.5 2 1.5

0.6 1.8 2

0.7 1.6 2.5

0.8 1.4 3

0.9 1.2 3.5

1.0 1 4


Which ordered pair is the best approximation of the exact solution?

Answer 1

Solve the system of equations:

$\left \{\begin{array}{l}y=-2x+3\\y=5x-1\end{array}\right.$

Equate right sides of bothe equations:

$-2x+3=5x-1,\\\\-2x-5x=-1-3,\\\\-7x=-4,\\\\x=\dfrac{4}{7},$

then

$y=-2\cdot \dfrac{4}{7}+3=-\dfrac{8}{7}+3=\dfrac{3\cdot 7-8}{7}=\dfrac{13}{7}=1\dfrac{5}{7}.$

You obtain the exact solution $\left(\dfrac{4}{7},1\dfrac{5}{7}\right)$ of the system of equations.

Since $\dfrac{4}{7}\approx 0.6$ and $1\dfrac{5}{7}\approx 1.7$, ordered pair (0.6,1.8) is the best approximation of the exact solution.

Answer: correct choice is B.

Answer 2

Answer: is b

Step-by-step explanation: