Question

Select the correct answer from the drop-down menu.

Consider the equations y=√x and y=x² -1
The system of equations is equal at approximately
A.(1.5,1.2)
B.(-1.5,-1.2)
C.(1.5,-1.2)
D.(-1.5,1.2)

Answer 1

Choice A.

Step.-by-step explanation:

y=√x

y=x² -1

Substituting the values in choice A:

1.2 = √1.5 = 1.2247 Approximately equal.

1.2 = (1.5)^2 - 1 = 1.25 Approximately equal.

Choice B.

-1.2 = √-1.5 which is imaginary so NOT this one.

Choice C

-1.2 = √1.5 = -1.2247

-1.2 = (1.5)^2 - 1 = 1.25 NO.

Choice D

We have the non real value √-1.5 again so NOT this one.

Answer 2

Answer: Option A

A.(1.5,1.2)

Explanation:

We have the following system of equations

`y=√(x)`

`y=x^2 -1`

the solution of the system will be all points that satisfy both equations at the same time

For (1.5,1.2)

`y=√(1.5)=1.2`

`y=(1.5)^2 -1=1.2`

Both equations are satisfied

Note that we can discard options B and D because the domain of the equation
`y =√(x)` does not include the negative numbers.

We can discard option C because the range of the function
`y =√(x)` does not include the negative numbers.

Finally the answer is the option A