Question

Solve the simultaneous equation 3x²-xy=0, 2y-5x=1​

Answer 1

Answer:

  (x, y) = (0, 1/2) or (1, 3)

Step-by-step explanation:

The first equation factors as ...

  x(3x -y) = 0

This has solutions x=0 and y=3x.

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x = 0

Using this in the second equation gives ...

  2y -0 = 1

  y = 1/2

  (x, y) = (0, 1/2) is a solution

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y = 3x

Using the expression for y in the second equation, we get ...

  2(3x) -5x = 1

  x = 1 . . . . . . . . . simplify

  y = 3x = 3 . . . . using x=1 in the first equation

  (x, y) = (1, 3) is a solution

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Interestingly, the (red line) graph of 3x^2 -xy = 0 produced by this graphing calculator has a "hole" at x=0, It says that point is (0, undefined). In a sense, y is undefined, in that it can be anything. A more appropriate graph would graph that equation as the two lines x=0 and y=3x.