Solve the following simultaneous linear and quadratic equations
x=y; 2x^2-y^=1
just replace y with x, since it says y = x
2x^2 - x^2 = 1
x^2 = 1
x = ±1
if x = 1, then y = 1
if x = -1, then y = -1
To solve the given system of simultaneous linear and quadratic equations, we can use the substitution method. Let's proceed step by step:
1. Start with the given equations:
x = y --------------(1)
2x^2 - y^2 = 1 -----(2)
2. Substitute the value of x from equation (1) into equation (2):
2(y)^2 - y^2 = 1
Simplifying further:
2y^2 - y^2 = 1
y^2 = 1
3. Take the square root of both sides:
√(y^2) = √(1)
y = ±1
4. Substitute the values of y into equation (1) to find the corresponding values of x:
For y = 1:
x = 1
For y = -1:
x = -1
5. So, the solutions to the given simultaneous equations are:
x = 1, y = 1
x = -1, y = -1
Therefore, the solutions to the simultaneous linear and quadratic equations are (x = 1, y = 1) and (x = -1, y = -1).