[x+2y=1 x+y²=4]

To solve the system of equations:

1. Rearrange the first equation to solve for x: x = 1 - 2y

2. Substitute the value of x in the second equation: (1 - 2y) + y² = 4

3. Simplify the equation: y² - 2y + 1 = 4

4. Rearrange the equation: y² - 2y - 3 = 0

5. Factorize the equation: (y - 3)(y + 1) = 0

6. Set each factor equal to zero and solve for y: y - 3 = 0 or y + 1 = 0 y = 3 or y = -1

7. Substitute the values of y back into the first equation to solve for x: x + 2(3) = 1 or x + 2(-1) = 1 x + 6 = 1 or x - 2 = 1 x = -5 or x = 3

Therefore, the solutions to the system of equations are: x = -5, y = 3 x = 3, y = -1