To find the solutions to the system of equations x² + y² = 5 and y = 2x, we can start by substituting the second equation into the first.
1. Begin with the equation:
x² + y² = 5
2. Substitute y = 2x into this equation:
x² + (2x)² = 5
3. Simplify:
x² + 4x² = 5
5x² = 5
x² = 1
4. Now take the square root of both sides:
x = ±1
5. Now, we find the corresponding values of y using y = 2x:
- If x = 1: y = 2(1) = 2
- If x = -1: y = 2(-1) = -2
So, the solutions to the system of equations are:
- (1, 2)
- (-1, -2)
In conclusion, the system of equations has two solutions: (1, 2) and (-1, -2).