Question

Which of the following graphs represents the solution(s) of the following system?
x2 + y = 7
x2 + y2 = 49

Answer 1

Answer:

2nd graph

Step-by-step explanation:

First of all, let's recognize that these 2 equations are that of a "parabola" and a "circle".

The equation of parabola is in the form $y=x^2$

If we have:

y = x^2 + b  where b is a constant, this means the parabola is shifted b units up.

Let's rearrange the first equation:

$x^2+y=7\\y=-x^2+7$

Note: the negative in front of x^2 makes it an "UPSIDE DOWN U SHAPED PARABOLA". Also this is shifted 7 units up.

Now, looking at the answer choices, we can eliminate:

1st and last  [ because these 2 are upward facing ]

Now, the equation of a circle. The general form is:

$x^2+y^2=r^2$

The equation given is in this form, so the radius is  $\sqrt{49}=7$

So that means, the circle is centered at origin and goes 7 units in all directions.

Between the 2nd and 3rd picture, we see that 2nd one is right since the circle coincides with the parabola up top and that is both 7 units as we have seen from our discussion.

Hence,

2nd graph is the correct one.

Answer 2

Answer:

Its the second one! I just took the assignment

Hope this helps!!