[x+2y=1 [x+y²=4

To solve the system of equations, we can use the method of substitution.

1. Solve the first equation for x: x + 2y = 1 x = 1 - 2y

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

3. Rearrange the equation to form a quadratic equation: y² - 2y + 1 = 4

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

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

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

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

   For y = -1: x + 2(-1) = 1 x -2 = 1 x = 1 + 2 x = 3

So the solutions to the system of equations are: x = -5 and y = 3 x = 3 and y = -1