Question

What are the solutions (coordinate points) to the system of equations?

Answer 1

(-2, 0), (0, 6)

Explanation:

A graphing calculator answers this easily. (See attached.) Solutions are (-2, 0) and (0, 6).

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Equate the expressions for y and solve the resulting quadratic.

x^2 +5x +6 = 3x +6

x^2 +2x = 0 . . . . . subtract 3x+6 to put in standard form

x(x +2) = 0 . . . . . . factor

Values of x that make this true are x=0 and x=-2. The corresponding values of y are most easily found using the linear equation for y:

y = 3·0 +6 = 6 . . . . . (x, y) = (0, 6) is a solution

y = 3(-2) +6 = 0 . . . . (x, y) = (-2, 0) is a solution