Which system of equations can be graphed to find the solution(s) to 4x² = x² - 7?

Solution:

The system of equations which can be graphed to find the solution to 4x² = x² - 7 are the following:

f(x) = 4x² --- (1) and 

g(x) = x² - 7 --- (2)

The solutions to the above can be examined by drawing their respective graphs which have been presented below:

It is apparent that the two graphs are not intersecting and hence have no common solutions. 

Algebraically also if we solve the two equations we get :

⇒ 4x² = x² - 7

⇒ 3x² = -7

⇒ x = i√7/3 which is an imaginary solution

Which system of equations can be graphed to find the solution(s) to 4x² = x² - 7?

Summary:

The solution(s) to 4x² = x² - 7 do not exist which is apparent from the graphs plotted for the two curves 4x² and x² - 7.