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17 December, 19:24

Solve the system of equations: y=2x-5. y=x^2-5

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  1. 17 December, 20:20
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    (0, - 5) and (2, - 1)

    Step-by-step explanation:

    Since both equations have already been solved for y, the substitution method is the easiest approach here. Set the two equations equal to each other:

    y = 2x - 5 = x^2 - 5 = y

    Focusing on the variable x only, we get 2x - 5 = x^2 - 5.

    Adding 5 to both sides results in 2x = x^2.

    Factoring this result, we get x (2 - x) = 0, whose solutions are

    x = 0 and x = 2.

    Now find the corresponding y-values:

    If x = 0, then y = 2 (0) - 5, or y = - 5;

    If x = 2, then y = 2 (2) - 5, or y = - 1

    Writing the solutions as coordinate pairs: (0, - 5) and (2, - 1)
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