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TheDoges
28.06.2019 •
Mathematics
What is the solution of quadratic system of equations ?
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Ответ:
(- 1, 1) and (- 5, - 35)
Step-by-step explanation:
since both equations express y in terms of x, equate the right sides
x² + 15x + 15 = - x² + 3x + 5 ( subtract - x² + 3x + 5 from both sides )
2x² + 12x + 10 = 0 ( divide all terms by 2 )
x² + 6x + 5 = 0 ← in standard form
(x + 1)(x + 5) = 0 ← in factored form
equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x + 5 = 0 ⇒ x = - 5
substitute these values into either of the 2 equations and solve for y
x = - 1 : y = (- 1)² + 15(- 1) + 15 = 1 - 15 + 15 = 1 ⇒ (- 1, 1 )
x = - 5 : y = (- 5)² + 15(- 5) + 15 = 25 - 75 + 15 = - 35 ⇒ (- 5, - 35 )
None of the given options
Ответ:
y = -⅔x + ²²/₃
Step-by-step explanation:
1. Calculate the slope of EF
Assume E is at (-2, 5) and F is at (1, 3).
m₁ = (y₂ - y₁)/(x₂ - x₁) = (3 - 5)/(1 -(-2)) = -⅔
2. Calculate the slope of the parallel line
m₂ = m₁ = -⅔
3. Calculate its y-intercept
y = mx + b
6 =-⅔(2) + b
Simplify
6 = -⁴/₃ + b
Add ⁴/₃ to each side
b = 6 + ⁴/₃ = ¹⁸/₃ + ⁴/₃ = ²²/₃
The y-intercept is at (0,²²/₃).
4. Write the equation for the line
y = -⅔x + ²²/₃
The diagram shows EF in red. The parallel line in black passes through (2, 6) with a y-intercept at (0,²²/₃).