Solve algebraically the simultaneous equations x^2 +y^2 = 25, y – 3x = 13
- Rearrange y - 3x = 13y = 3x + 13 2. Substitute into x^2 +y^2 = 25x^2 + (3x + 13)^2 = 25 3. Expand bracketx^2 +(9x^2 + 39x +39x +169) = 25 4. Form quadratic equation 10x^2 + 78x + 144 = 0 (Dividing by 2 makes factorising easier)5x^2 + 39x + 72 = 0 5. Factorise (5x + 24)(x + 3) = 0 6. Solve for xx = -24/5, x = -3 7. Substitute values of x into y = 3x +13 to find y values x = -24/5, y = -7/5x = -3, y = 4
