Question

Please help me with this problem

Answer 1

9514 1404 393

Answer:

  (x, y) = (-3, -13) or (-8, -23)

Step-by-step explanation:

The values for y can be equated and the resulting quadratic solved by factoring.

  2x -7 = x^2 +13x +17

  0 = x^2 +11x +24 . . . . . . subtract 2x-7

  0 = (x +8)(x +3) . . . . . . . .factor*

The values of x that make these factors zero are x=-8 and x=-3. The corresponding values of y are ...

  y = 2(-8) -7 = -23

  y = 2(-3) -7 = -13

The solutions are ...

  (x, y) = (-8, -23) and (-3, -13)

_____

* The constants in the binomial factors are factors of 24 that total 11. You know that ...

  24 = 1×24 = 2×12 = 3×8 = 4×6

The sums of these factors are 25, 14, 11, 10. The factors 3 and 8 are the constants in the binomial factors of the quadratic.

"24" is the constant in the quadratic. "11" is the coefficient of the x term.