Solve: x^2 + y^2 = 25 y - 3x = 13
Equation 1) x2 + y2 = 25 Equation 2) y - 3x = 13 First you need to substitute a variable so there is only one unknown in the equation: 2) y = 13 + 3x Substituting this into equation 1) gives: x2 + (13 + 3x)2 = 25Multiplying out the brackets: x2 + 169 + 78x + 9x2 = 25 Simplifying the equation: 10x2 + 78x + 144 = 0 Dividing the entire equation by 2: 5x2 + 39x + 72 = 0 Next find the factors of 5 - 1,5 and 72 (1, 72. 2, 36. 3, 24. 4, 18...) Find which combination of factors, when multiplied add together to make 39: 1,5 and 3, 24 : Thus(5x + 24)(x + 3) = 0 Therefore: x = -3 and x = -24/5 Substituting these values into equation 2 gives: x = -3 y = 4 and x = -24/5 y = -7/5
