Solve the simultaneous equations : x^2 + y^2 = 13 and x = y - 5 .

Below is the solution to the aforementioned question. In order to solve a simultaneous equation, one has to write one of the unkown variables in terms of the other. In this case, x was already written in relation to y, which means we can replace x in the first equation with y - 5. This allows us to have an equation with only one unkown variable, y. We solve this equation and we end up with two possible solutions for y. We find out x in both those solutions and we have our answers. Below is the mathematical solution as well. x2+ y2 = 13 x = y - 5 (y - 5)2 + y2 = 13 (y - 5)(y - 5) + y2 = 13 y2-5y - 5y + 25 + y2 = 13 2y2-10y + 25 = 13 2y2-10y + 12 = 0 y2-5y + 6 = 0 (y - 3)(y - 2) = 0 y1= 3 and y2 = 2 x1 = (3) - 5 and x2 = (2) - 5 x1 = -2 and x2 = -3

Answered by Sebastian G. Maths tutor

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There are a total of 50 apples and pears (apples + pears) in a large basket. If the total number of apples was doubled and the total number of pears was tripled, these two numbers would add up to 130. How many apples and pears are in the basket?


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