solve this by elimination method
x^2 + y^2 =1
2x^2 +2y=2
Answer (1)
Answer:Here's how to solve the system of equations using the elimination method: 1. Simplify the second equation:Divide the second equation by 2: - x² + y = 1 2. Rearrange the equations:Equation 1: x² + y² = 1Equation 2: x² + y = 1 3. Eliminate x²:Subtract Equation 2 from Equation 1: - (x² + y²) - (x² + y) = 1 - 1This simplifies to: y² - y = 0 4. Solve for y:Factor out y: - y(y - 1) = 0This gives us two possible solutions: - y = 0 - y = 1 5. Substitute y values back into either original equation to find x:If y = 0: Substitute into Equation 1: x² + 0² = 1 x² = 1 x = ±1If y = 1: Substitute into Equation 1: x² + 1² = 1 x² = 0 x = 0 Solution:The system of equations has three solutions: - (x, y) = (1, 0) - (x, y) = (-1, 0) - (x, y) = (0, 1)
