Which system of equations can be graphed to find the solution(s) to x2 = 2x + 3?

a. y=x2+2x+3/y=2x+3
b. y=x2-3/y=2x+3
c. y=x2-2x-3/y=2x+3
d. y=x2/y=2x+3

ANSWER

The correct answer is

and


EXPLANATION

The given equation is



If we consider this equation as a single equation, then we can use methods such as factorization, completing the squares, or the quadratic formula to solve it.

For instance using the method of factorization we proceed as follows,










Meaning when we graph the function

, it will intersect the x-axis at


However, if we consider the equation to be two different systems combined, that is the equation of the straight line


and the equation of the basic quadratic function


Then the solution to

is the intersection of the graph of the straight line and the graph of the quadratic curve.

That is the x-coordinates of the points of intersection are the solutions.

See graph.

1.17+3.99a. you combine the terms with a to create 3.99 and the 1.17 stays because it has no like terms or a variable