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17 February, 04:54

What is the smallest value of y in the solution set to the system of equations below?

y=x^2+6x+23

y=18x-12

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Answers (1)
  1. 17 February, 05:01
    0
    The smallest value of y in the given two equations is 78

    Step-by-step explanation:

    Given as:

    The two equation is given as:

    y = x² + 6 x + 23 ... 1

    y = 18 x - 12 ... 2

    Now, solving both equations

    putting the value of y from eq 2 into eq 1

    So, x² + 6 x + 23 = 18 x - 12

    Or, x² + 6 x + 23 - 18 x + 12 = 0

    Or, x² - 12 x + 35 = 0

    Or, x² - 5 x - 7 x + 35 = 0

    Or, x (x - 5) - 7 (x - 5) = 0

    Or, (x - 5) (x - 7) = 0

    ∴ x = 5, 7

    Now, for smallest value of y, take x = 5

    ∴ put the value of x in eq 2

    So, y = 18 x - 12

    I. e y = 18 * 5 - 12

    Or, y = 90 - 12

    ∴ y = 78

    Hence, The smallest value of y in the given two equations is 78. answer
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