[x+2y=1 [x+y²=4

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

First, let's solve equation 1 for x: x = 1 - 2y

Now substitute this value of x into equation 2: (1 - 2y) + y^2 = 4

Rearrange the equation and make it a quadratic equation: y^2 - 2y - 3 = 0

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

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

If we solve y - 3 = 0, we get y = 3. If we solve y + 1 = 0, we get y = -1.

Now substitute these values of y back into equation 1 to find x: For y = 3: x + 2(3) = 1 x + 6 = 1 x = -5

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

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