{x+2y=1 x+y²=4

To solve the system of equations:

1. x + 2y = 1
2. x + y^2 = 4

We can use the method of substitution or elimination. Let's try substitution first.

From equation 1, we can express x in terms of y: x = 1 - 2y

Substitute this value for x in equation 2: 1 - 2y + y^2 = 4

Rearrange the equation to get a quadratic equation: y^2 - 2y - 3 = 0

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use factoring:

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

So, either y - 3 = 0 or y + 1 = 0.

If y - 3 = 0, then y = 3. Substitute this value of y back into equation 1 to find x: x + 2(3) = 1 x + 6 = 1 x = -5

So, one solution is x = -5 and y = 3.

If y + 1 = 0, then y = -1. Substitute this value of y back into equation 1 to find x: x + 2(-1) = 1 x - 2 = 1 x = 3

So, another solution is x = 3 and y = -1.

Therefore, the system of equations has two solutions: (-5, 3) and (3, -1).