Solve the system of equations y=3x+2 y=x2-4x+2

  (x, y) = (0, 2), (7, 23)

Step-by-step explanation:

I find a graphing calculator to be a quick and easy tool for finding the solution. The attached shows the solutions to be ...

  (x, y) ∈ {(0, 2), (7, 23)}

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Equating the expressions for y, we have a quadratic equation. It can be put into standard form and factored.

  3x +2 = x^2 -4x +2

  0 = x^2 -7x = x(x -7)

Solutions are values of x that make these factors zero, so are ...

  x = 0   and    x = 7

Corresponding values of y are ...

  y = 3·0 +2 = 2 . . . (0, 2) is one solution

  y = 3·7 +2 = 23 . . . (7, 23) is the other solution

step-by-step explanation:

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