Question

Nevin made tables of values to approximate the solution to a system of equations. First he found that the x-value of the solution was between one and two, and then he found that it was between one and 1.5 next, he made his table.

Answer 1

Answer:

The correct option is B.

Step-by-step explanation:

The given equation are

$y=4x-3$

$y=-5x+9$

On solving both the equation, we get

$4x-3=-5x+9$

$4x+5x=9+3$

$9x=12$

$9x=\frac{12}{9}=\frac{4}{3}$

Put this value in the given equation.

$y=4(\frac{4}{3})-3$

$y=\frac{16}{3}-3$

$y=\frac{16-9}{3}$

$y=\frac{7}{3}$

The solution of the given system of equation is

$(\frac{4}{3},\frac{7}{3})=(1.333,2.333)\approx (1.3,2.3)$

The best approximation of the exact solution is (1.3,2.3). Therefore the correct option is B.

Answer 2

Answer:

B. (1.3, 2.3)

Step-by-step explanation:

To find approximate solution of the system of equations, we need to equivate the two given equations and solve for x and y.

y = 4x - 3 and y = -5x + 9

4x - 3 = -5x + 9

Isolating the variables and constants, we get

4x + 5x = 9 + 3

9x = 12

Dividing both sides by 9, we get

x = 12 ÷ 9

x = $\frac{4}{3}$

x = 1.3

Now plug in x =  $\frac{4}{3}$ in the equation y = 4x - 3 to find the value of y.

y = 4( $\frac{4}{3}$)  - 3

y = $\frac{16}{3}$ - 3

y =  $\frac{16 - 9}{3}$

y =  $\frac{7}{3}$

y = 2.3

So, x = 1.3 and y = 2.3 is the approximate solution.

Therefore, answer is B. (1.3, 2.3)