What is the solution set for this linear-quadratic system of equations?
2 answers:
For this type of solution set, it is easiest to substitute one equation into another before we factor the resulting equation out...
y = x² - x - 12 (using this, we already know what y is equal to)
y - x - 3 = 0 (substitute the first value of y into this equation and simplify)
(x² - x - 12) - x - 3 = 0 (drop the parentheses)
x² - x - 12 - x - 3 = 0 (combine like terms)
x² - 2x - 15 = 0 (now we can factor -15)
(x - 5) (x + 3) = 0 (set each to equal 0)
x - 5 = 0 x + 3 = 0
x = 5 x = -3 (now we have the solution to the system)
Y - x - 3 = 0
y = x + 3
y = x^2 - x - 12
x + 3 = x^2 - x - 12
x^2 - x - 12 - x - 3 = 0
x^2 - 2x - 15 = 0
(x - 5)(x + 3) = 0
x - 5 = 0 y = x + 3
x = 5 y = 5 + 3
y = 8
x + 3 = 0 y = x + 3
x = -3 y = -3 + 3
y = 0
so ur solutions are : (5,8) and (-3,0)
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