Final answer:
To find the solution(s) to the equation 4x^2 = x^2 + 7, we transform it into two separate equations, y = 3x^2 and y = x^2 + 7, which correspond to the options A and B, respectively. These equations, when graphed on the same coordinate plane, show the solution(s) at their intersection points.
Step-by-step explanation:
To determine which system of equations can be graphed to find the solution(s) to the equation 4x^2 = x^2 + 7, we first need to transform the given equation into two separate equations that can be graphed. We do this by isolating y in each equation to make them comparable to the form y = mx + b or y = ax^2 + bx + c which are the standard forms for linear and quadratic equations, respectively.
Starting with the given equation, we can rewrite it as 4x^2 - x^2 = 7 and obtain 3x^2 = 7, and then we assign y to both sides of the equations resulting in two separate equations:
- y = 3x^2 (from the left side of the original equation)
- y = x^2 + 7 (from the right side of the original equation)
The correct choices from the given options that represent these two equations are:
- A) y = 3x^2
- B) y = x^2 + 7
Thus, the correct system of equations to graph to find the solution(s) is a combination of A) and B). When graphed on the same coordinate plane, the intersection point(s) of the two curves will represent the solution(s) to the original equation