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math b

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solve each system of equation algebraically:
x2+y2=18
x+y=4

  • math b -

    Do you mean the circle
    x^2+y^2 = 18 ?

  • math b -

    yes

  • math b -

    Making that assumption, we are looking for where the straight line:
    y = -1x + 4
    which has a slope of -1 and goes through (0,4) and (4,0)
    hits the circle with center at the origin and radius 3 sqrt 2 which is about 4.24
    Sketch a graph so we will get an idea of how the solution should look.
    So
    substitute y = -x + 4 into the circle
    x^2 + (-x+4)^2 = 18
    x^2 + x^2 - 8 x + 16 = 18
    2 x^2 -8 x -2 = 0
    x^2 - 4 x -1 = 0
    x = (1/2)[ 4 +/- sqrt (16 +4)]
    x = (1/2) [ 4 +/- 2 sqrt 5]
    x = 2 +/- sqrt 5
    find the y for each of those x values

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