Consider the following system of equations.
y=6x2+1
y=x2+4
which statement describes why the system has two solutions?
a. each graph has one y-intercept, which is a solution.
b. each graph has one vertex, which is a solution.
c. the graphs of the equations intersect the x-axis at two places.
d. the graphs of the equations intersect each other at two places.

  D. The graphs of the equations intersect each other at two places.

Step-by-step explanation:

The definition of a solution of a system of two equations in two variables is a point where the graphs intersect. A system of equations having graphs that intersect each other will have as many solutions as there are intersection points. If the graphs intersect in two places, there will be two solutions.

gdp is the best phrase!

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1