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