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

B. (1.3, 2.3)

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 =
`(4)/(3)`

x = 1.3

Now plug in x =
`(4)/(3)` in the equation y = 4x - 3 to find the value of y.

y = 4(
`(4)/(3)`) - 3

y =
`(16)/(3)` - 3

y =
`(16 - 9)/(3)`

y =
`(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)

Answer 2

The correct option is B.

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=(12)/(9)=(4)/(3)`

Put this value in the given equation.

`y=4((4)/(3))-3`

`y=(16)/(3)-3`

`y=(16-9)/(3)`

`y=(7)/(3)`

The solution of the given system of equation is

`((4)/(3),(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.