Math CentralQuandaries & Queries


Question from kyrie, a student:

simultaneous equation

4x + 3y = 21
2x * y = 8


Let me try a similar problem.

3x - 6y = 14
3xy = 5

I would start by solving the second equation for y, thus

y = 5/(3x).

Now substitute this value for y in the first equation which becomes

3x - 6 times 5/(3x) = 14 or
3x - 10/x = 14

Multiplication of both sides by x gives

3x2- 10 = 14x or
3x2 - 14x - 10 = 0

Solve for x. Once you have x you can substitute into either of the two given equations to find y.

Since this last equation is a quadratic you may find two values of x and each will give a corresponding y value. Make sure you verify each answer you get is actually a solution to the problem.

I hope this helps,

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