Answer:
To solve the given simultaneous equations: 2x + y = 5 ------------(1) 2x^2 + y^2 = 11 ------------(2)
We can use the method of substitution to solve the equations.
Substituting y = 5 - 2x from equation (1) into equation (2), we get: 2x^2 + (5 - 2x)^2 = 112x^2 + 25 - 20x + 4x^2 = 112x^2 + 4x^2 - 20x + 25 - 11 =
simplifying, we get: 6x^2 - 20x + 14 = 0
Dividing by 2, we get: 3x^2 - 10x + 7 = 0
Factorizing, we get: (3x - 7)(x - 1) = 0
Solving for x, we get: x = 1 or x = 7/3
Now substituting x = 1 in equation (1), we get:2(1) + y = 5y = 5 - 2y = 3 Therefore, one solution is x = 1 and y = 3
Substituting x = 7/3 in equation (1), we get: 2(7/3) + y = 5y = 5 - 14/3y = 1/3
Therefore, the other solution is x = 7/3 and y = 1/3
Hence, the solutions of the given simultaneous equations are x = 1 and y = 3 or x = 7/3 and y = 1/3.
Explanation:
Hope this helped!! Have a great day/night!!