Solve the simultaneous equations: x^2 + y^2 = 5 and y = 3x + 1

x² + y² = 5 1y = 3x + 1 2Inserting 2 into 1: x² + (3x +1)² = 5 Expanding the brackets: x² + 9x² + 3x + 3x + 1 = 5Collecting like terms: 10x² + 6x - 4 = 0Using the quadratic formula: x = (-6 ± √(6² - 4 * 10 * -4))/(2 * 10)Simplifying: x = ( -6 ± √(36 + 160))/20Simplifying further: x = (-6 ± √196)/20Solving for x: x = (-6 ± 14)/20 x₁ = (-6 + 14)/20 or x₂ = (-6 - 14)/20 x₁ = 8/20 or x₂ = -20/20 x₁ = 0.4 or x₂ = -1Substituting x₁ and x₂ into 2: y₁ = 3x₁ + 1 or y₂ = 3x₂ + 1 y₁ = 3(0.4) + 1 or y₂ = 3(-1) + 1 y₁ = 1.2 + 1 or y₂ = -3 + 1 y₁ = 2.2 or y₂ = -2Rewrite answers: x₁ = 0.4 and y₁= 2.2 x₂ = -1 and y₂ = -2