[x+2y=1 [x+y²=4

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

Let's solve the first equation for x:

x + 2y = 1 x = 1 - 2y

Now substitute this value of x into the second equation:

(1 - 2y) + y² = 4

Rearrange this equation and solve for y:

y² - 2y - 3 = 0

Factoring this quadratic equation, we have:

(y - 3)(y + 1) = 0

Setting each factor equal to 0, we get:

y - 3 = 0 --> y = 3 y + 1 = 0 --> y = -1

Now substitute these values 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

Therefore, the solution to the system of equations is x = -5, y = 3 and x = 3, y = -1.